I think math will go the way of biology. Biologists enjoy untangling the infinitely complex mechanisms of life, including the brain, and win Nobel Prizes for discoveries like "how water enters a cell," rather than "constructing the first-ever cell capable of absorbing water."
No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch."
True but mathematicians chose maths and not biology for a reason. It is like golf could go the way of chess if people developed perfect "hole in one" augmentation for their eyes/brains/muscles. But that isn't why people learned anf loved golf. I guess we will have one less discipline. But maths is a big one to lose, unlike say ancient chariot building (which has other artisanal equivalents).
Golf as a sport is competitive, very much like boxing or chess. It's human vs human; a machine doing a hole in one would ruin golf no more than the invention of a wrecking ball machine ruined boxing.
Mathematics is a fundamentally cooperative match vs reality. Many mathematicians, AFAICT, saw their key skill in manipulating a wide range of highly abstract notions. Now machines just got too good at this skill, and they can work 24/7. This may feel terrifying for some. Others would bet that machines coöperating with humans will be more successful than pure machines, so they feel empowered. What's beyond doubt is that the entire field is being shaken.
They are not very much alike at all. This is a very poor analogy.
In boxing, chess and many other competitive sports, the actions of one player directly influence and have an effect on the other player. Golf is merely a parallel challenge, where both are playing against each other but not influencing each other directly (sure maybe there are some psychological effects that can occur between the players, but no strategical impact by the actions of one player on the other).
>no strategical impact by the actions of one player on the other
The players know if they're ahead or behind, which affects how much risk to take. Do you take the safe shot, or go for the tricky shot that could potentially save you a stroke if you get it right but could lose you more if you fail?
> (sure maybe there are some psychological effects that can occur between the players, but no strategical impact by the actions of one player on the other).
You'll see a golfer perform at least a few strokes different depending on their partner, and at a pro level that's the difference between "in the money earning an extravagant living" and "washed out on day one, thinking about taking a different job"
You can chose to do whatever you like, but that does not mean others now or in the future are obliged to pay you to do what you like if it's no longer economically viable or socially willed.
We can and should have it as something that people do in the future because we have the resources for everyone to do so.
Did humanity ever come up with something more advanced than themselves, including their brain? Superintelligence is a different beast entirely to anything from human history.
Unless I'm misreading OPs post, he was commenting that this very advanced technological era would bring prosperity and then humanity can afford to pay people to do what they like.
And my comment was cynical: when has lots of prosperity lead directly to its fair distribution? Almost every redistribution process required lots of people dying, first.
Perhaps some people chose math because they were very good at it, they could understand one shot the difficult concepts and have not enough money to study other subjects because you have to move city or pay a lot. Those kind of people can move to others field if economics conditions are favourable.
It sounds like what these people are very good at is what AI is becoming very good at, so they will be losing their economically valuable edge. For example, it used to be that many math and physics majors went into software development.
Synapses in the brain are affected by quantum effects that lower or increase the threshold for firing. Thus they are not deterministic and people do indeed have influence over their own behavior.
1. This goes against the prevailing view of neuroscientists. Quantum indeterminacy is generally thought to be irrelevant to brain function.
2. Quantum randomness is the very opposite of control over your behavior. Instead of doing what you want, your neurons randomly misfire sometimes. That describes an illness where you lose control over whatever is misfiring. For quantum effects to represent your will, they couldn't be truly random (nor even statistically random), and that goes against everything we know about quantum mechanics.
On a small enough timeline over simple things like "piss in street zero fucks or find toilet?"
On long enough timelines involving too many variables; either other peoples waves vibrating through the economy or politics; all bets are off.
We tend to over estimate the future based on a lizard brain ability to estimate the next few moments; a handy survival tool when trying to determine if we recognize the noise we just heard behind a rock
Did you predict covid in 2020 from 1996? All human society stats are mutable and trend towards zero.
But Nostradamus and Hari Seldon type long range forecasting is fanatasy
This is an interesting perspective and maybe the most interesting argument in the thread.
But why can't a hyper-intelegent AI also do this biology-esque math work of explaining its work to feeble humans?
It is easy for a genius to have theory of mind over an idiot but not vice-versa. So it should be easier for a genius AI to explain its work to an idiot human than for an idiot human to dissect the work of an genius AI.
Also, we're not talking about solutions that are arrived though an evolutionary/statistical process like explaining the design of an organism or the weights of an LLM. We are talking about solutions that are arrived through lingual/textual/rational processes like mathematics. So it's fundamentally a different mode of thinking.
It's not that we have "a brain to study", it's like if we had an "explaination of how a brain works" to study.
The task of breaking down these AI proofs is not translating and analyzing a fuzzy real-world system into a hard logical system (like in biology), but in translating a hard logical system into a simpler hard-logical system we can understand.
This assumes AIs will become more capable than humans in every way. If so, then yes, there's little point for people to be part of the discovery process other than to tell the AI what to investigate next.
But I think a more likely scenario is that we don't solve "general intelligence" and AIs remain these incredibly capable "tools" that can solve navier stokes but completely lack sense in other situations.
In such a scenario there is considerably more room for human creativity.
The burden of proof is on you: name just five examples.
I am very highly gifted as a qualifier and quite frankly I never had more interesting thought exchanges than with an ego-free AI.
Statistics work also for human AI aka IQ, and I am super bored and partly drained by the lack of speed and creativity in many intellectual areas in which I was or am working.
This is not to blame anyone for their genetics however, it is a valid difference in processing speed.
In short: there are very few people by definition above two standard deviations. AI allowed me to replicate or create fantastic interactions at will.
Especially not taking offense when personal communication preferences like bluntness play a role is an often overlooked social competency of AI. Instead of nonsense like “open communication” these interactions are never ego-dependent.
It is like talking to Spock: he just doesn’t take offense and tells you in an objective way why: he is not a human being and doesn’t think (not feel) that feelings should get in the way of an argument.
Most low IQ people take offense and go on to ridicule and use shaming tactics instead of simply stating: I don’t know.
Instructing someone to always state this fact and seeing the result is another social skill humans lack.
It seems that we as species are not open to the mirror we are looking at. We take revenge when someone has an evolutionary advantage over us: instincts kick in instead of brains.
We are wired this way.
AI is something that I admire. So much to learn from.
Name five examples of what, exactly? They are talking about theoretical scenarios. There is no burden of proof because no concrete claim was made. He did not say “x will happen” or “x is true"; he posited an opinion. Furthermore, by your own standards, you must provide five concrete examples of being “very highly gifted as a qualifier."
Additionally, what you are admiring is merely a probability engine; it is not intelligent in any sense of the word, let alone Spockian in nature (perhaps more closely aligned to Data, albeit horribly primitive by comparison), and given current technology, it never will be. It is not a mirror, because a mirror reflects reality. LLMs don’t do that; they reflect the guardrails baked into their model and the prompts given. It is incredibly easy to make an LLM into a “yes-man” due to RLHF, and it is even easier to get it to seize when you talk about even mundane topics that go against the narratives foisted upon it.
Overall, an LLM is all too happy to have a brown nose and make you feel important, because it is trained to do so during its creation. If people say you are difficult to talk to, and the LLM is unbothered, then that is merely because an LLM has no concept of patience and does not calculate for cost-benefit. That makes them good for explaining dense topics, but it also means they never understand these topics, and even the highest-end models cannot currently produce perfect logic. Hence why expertly written human code trumps LLM code, or why some LLM proofs are already being proven wrong/being revised to be more concise.
I would bet that there are some proofs whose simplest form are simply incomprehensible to humans. Explaining them in terms a human could possibly understand is a fool's errand. However the theorem itself may be much simpler, and the theorem is the thing that's most worth translating.
Attempting to translate the proof is valuable, but we have to be realistic about what is and isn't possible.
I like this analogy! I think it relates to what he was saying in the video about theorems now being 'data points' that you observe and build into wider theories. The change is that now the theorem proving itself, which used to require deep understanding, can now be done very quickly. There are lots of parallels to when genAI for image generation came out, artists were frustrated their work is seen as just an end result - AI obliterates the elegance and the process.
I am not a mathematician, but I imagine it will provide a huge landscape of possibilities to explore, and be a very different field. Almost like an observational science with links to all kinds of other disciplines. Maybe it reduces the satisfaction from proofs, but people climb mountains that other people have climbed, because they learn a lot on the way.
As I commented in another thread: I just finished a very short story by Ted Chiang - 'The evolution of Human science' it starts at the point where it's 25 years since humans contributed a scientific paper because 'meta humans' now handle all research, and communicate digitally such that humans can only get a low fidelity report of what the agents actually know, and the endeavour to understand has become like a best effort archeological like hobby for interested humans. The story assumes that the 'meta humans' will always act in humans best interests. I believe it's from 2002, it's incredibly precient (The stories of your life and others is the collection the story is in. Many of them are very relevant to modern AI actually).
What makes you think that humans will be better at this than AI? At least in biology, you need to conduct physical experiments, which excludes pure AI. But math?
> I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
> Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
> I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
What one wants to do and what is economically valuable are different. Be glad we live(d) in an era where those coincided because for most of human history people had to do the work they got, not that which they wanted.
I think you are mistaking 'happiness' with 'employment' here. The leather worker may adapt to the new environment to become a factory site manager. But there's no guarantee that this leads to happiness.
Also you should bear in mind, adaptation is a young man's game. Retraining is possible, but companies typically don't hire interns in their 50s. My Dad ended up as a postal worker when he left his career as a humanities academic at 55, no highly skilled jobs would take him (he did prefer it though haha).
> > But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
...Or you can keep working on your handbags & refine your styles & qualities, using your expertise & experience as value adds.
The existence of the factory did not wipe out the boutique craftsman.
> > A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place.
A craft wasn't ripped away from you: The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
The only step required to restore it is to ignore the contributions of others that use it. And your desire to do so will be valid & consistent.
But similarly as to how you want to be validated on your feelings of 'the craft being ripped from you', you don't get to impose that belief onto others to rip their use of LLMs away from them if they want to do so, lest you want to invalidate their feelings as a consequence.
> The existence of the factory did not wipe out the boutique craftsman.
But... it did? It's not like there are lot of horse carriages out there or, for a more recent example, plenty of Cobol developers. Or for a closer example, there used to be plenty of shoemakers when I was young and yet now I know of exactly one.
> The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
At the risk of stating the obvious: just because I can be a woodcarver as a hobby it doesn't mean it's the same as making a living out of woodcarving because doing something I consider enjoyable for a living is not the same as doing it exclusively as a hobby. If I fire a Cobol programmer knowing full well they'll have to work at their local supermarket until retirement, telling them "you can still program in your free time" will not bring them comfort.
Horse carriages were replaced by a superior technology, that has literally zero bearing on the discussion and actively weakens your argument. Also they are still made to demand, but that demand shrunk dramatically when people stopped needing horses.
The entire analogy is flawed though, and this is why: a market still exists for handmade objects. Factories make cheap clothing/objects, but handmade bags/woodworking are still deeply valued and there are people who still make their living in woodworking and other fields. Factories did bring some professions to near-extinction, but that doesn’t mean there is nothing left of them. In fact, many utilize factory techniques and tools in their work to ease costs, like lathes.
As for COBOL, it was mostly phased out because it’s Hell to program for and other languages like Python allow for faster dev time (for both good and bad). COBOL programmers still exist, and you’re honestly unlikely to fire that COBOL programmer because you need them to maintain mission-critical infrastructure. However, because you’re not actively building new COBOL programs, you also don’t need any more than that one. For compliance reasons it also needs to be a human, because a lot of surviving COBOL code is medical or financial in nature.
> the issue is that there are no value adds from humans anymore if the LLM is smarter than everyone
The value adds (from the view of humans wanting it) come from:
1) a human understanding concept X & thus can communicate about X; or
2) finding alternate routes to X that make it easier for humans to get there.
(1) is human-centric & thus non-replaceable, since the requirement of a human is what gives it the value add.
(2) is similar to how there can be many paths to deriving the Pythagorean theorem. None of the existing paths devalue the others, but they each allow those with different perspectives to reach the same destination.
right, so mathematicians will be communicating someone else's discoveries instead of making their own. notwithstanding whether that's an interesting job or not (I know, it's not part of the discussion), why wouldn't LLMs be able to do that with enough RLHF?
And why would a human be able to come up with a proof an LLM can't? I get your point but the new paths and perspectives could probably all be derived by prompting "prove xyz statement" a few times in fresh chats.
It's not really missed though. He does spend a good amount of time saying that it'll be a problem for many. Whether it's most of professional mathematicians is an open question I think.
If your job was previously mainly following instructions from SO, and this has now been replaced by Claude - your employment prospects are not looking good right now. You're just a middle-man between your PM and the codebase that possibly doesn't need to exist for long.
> Translation: my fragile ego is totally dependent on being overpaid for typing instructions I found on stackoverflow
I'm confused. Your comment's shitty tone implies you're overwhelmingly in favor of LLMs. That's copy-pasting not just on steroids, but on crack cocaine. So what point are you trying to make?
If you read carefully I don’t suggest you to base your personality on producing code at all. Whether it comes from SO or Claude, there is no proud in any of these. Let’s be adults and be proud of solved problems and users using our products.
It might just not matter what Tao and everyone of them thinks if the people in charge of the budget think otherwise.
If we don't come to a global agreement (of course only the top 10 gdp countries, lets ignore all the 3th world which we done for ages anyway) on how to create/spend money for this type of things, we will get in problems.
And even if the winners of this (ai companies/hyperscalers) will start 'gifting' universitys and budgets, thats not the solution.
There's never been a better time to go into [insert field that is presently being helped by AI, but not yet fully autonomously replaced, giving the false impression and hope that somehow that's the way it will continue in the future].
History has shown that a very potent tool can improved and changed industry entirely for the better. People now seems to be more negative than when atomic bomb was invented.
Looked what happened when crane was invented and not only more houses are built faster but also high rise building suddenly become feasible with more human being employed in the construction industry than ever.
> Why so negative? History has shown that a very potent tool can improved and changed industry entirely for the better.
AI isn't like any other historical tool or technology. Its qualitatively different. Flint axes or waterwheels or a plasma torches dont just suddenly appear everywhere, and then start getting rapidly (and likely recursively) better at the thing they do. While also mimicking innate human characteristics like complex language.
AI, computers, electricity, steam power, basic tools, and even fire all enabled in a dramatically faster rates of change compared to the immediately preceding era. You could also argue all also mimic certain human (or more broadly, animal) characteristics. I don't see what is truly unique to AI here. I'm not sure AI is even qualitatively unique from the computer, just the technology taken to it's logical conclusion.
Fundamentally I don't think "tool" is the right word for whatever generative AI is. Tools are normally designed with intention for a specific purpose, but AI systems are trained or grown.
To use an analogy, you can use a goat as a lawnmower - it'll keep the grass down for you. You could maybe even train it so it keeps it a specific length, but it's a goat - there's always a chance it will jump the fence or headbutt you or something else. It's an animal, not a tool. You can use AI as a tool, but that doesn't make it a tool.
Yes AI is arguably still software, but we have never seen programs with anything close to this level of flexibility and adaptability in software.
As another analogy, there's nothing special about neurons- their characteristics are broadly known and researchers have been able to simulate small numbers of them in computer models. However, when you have enough of them in the right structure, complex behaviours are possible which are never exhibited at the lower levels. There's nothing majorly different between the neurons in brains of a chimp and a human, but the capabilities and meta-capabilities are wildly different.
I think we see a similar step-change with generative AI systems.
> Flint axes or waterwheels or a plasma torches dont just suddenly appear everywhere, and then start getting rapidly (and likely recursively) better at the thing they do.
Trains. Building railroads made everything faster, including building faster trains, which facilitated making cars and trucks, which facilitated airplanes, etc.
Fairly sure that even today if you memory wipe all knowledge of trains and train building (including road trains, like in Australia) and vaporize all railroads, locomotives, rail wagons, train stations, etc, it would set us back 50 years.
The crane is a poor analogy to a general purpose thinking machine that is intended to replace human effort and reasoning at all levels of abstraction in all cognitive endeavors.
Cranes were invented like 3000 BC, and their first known use in construction is in 600 BC. I can't think of a much slower development than the invention of cranes leading to the construction of high rise buildings
I feel like the power loom is a better comparison. It put hand weavers out of business over a short timespan, while revolutionizing how clothing is produced. It certainly empowered a lot of jobs surrounding clothing, until clothing was completely commoditization and is now a lot less well designed simply as a function of clothing as a category being a much cheaper product now
> Looked what happened when crane was invented and not only more houses are built faster but also high rise building suddenly become feasible with more human being employed in the construction industry than ever.
New inventions eventually benefiting the society has always been accompanied by new jobs being created on top of those inventions, a culture of trust built upon mastering those inventions and a market being formulated around demand and supply cycle for those inventions. It is different now[1], because we neither see incentives being created for humans to operate/manage AI-led jobs (because utilizing such a thing is far more unfavorable than outsourcing due to economic incentives, duh) nor a foreseeable market stability for ever such thing to occur.
Are you sure we don't see AI operating roles grow?
Afaik the SWE roles that are being cutoff are mainly at the companies (faangs) shuffling the investments to GPUs and the rest of the economy (in the US) is not hiring because it's basically in a recession due to other economical reasons.
Anedoctiically I see the opposite in my neck of the woods and I have more work than before because of LLM since I basically transitioned to build LLM infrastructure
I'm a fairly heavy user of LLMs [1] but i'm probably in the "AI is just a tool" camp.
Are you of the view that LLMs have more potential than the internet? The internet has been around for so long that it's had time to have actual impact and yet it barely shows up in GDP. It still has so much untapped potential even yet. LLMs are too new to have amassed much impact yet, certainly not on the scale of the internet. But they have lots of potential still untapped. I just don't see how we get to even 5% GDP impact with them (either positive or negative). But i could be in a blind spot, genuinely curious to learn another view point.
[1] I've built all sorts with them. I've built various ML models but the only LLM i've built was effectively following a tutorial, nanochat
I think computers, internet and AI - all of them have impact - but they consume it by converting it into new structure. The benefits are in the infra not handed out to us individually. We might not see large changes on individual level, or the displaced work is replaced by management work for the automations and raising baselines push us to do more. We now have data centers, fiber backbone, GPUs, models, apps and open source projects, yet we still only have 24 hours a day.
The AI of today is just a tool, albeit a very powerful one. But I don't think it's a big step for it to reach a level where the majority of humans will be unable to to meaningfully contribute to the economy ten years from now.
The fear of the atomic bomb is relatively instant (at "best") or as bad as finding out you have cancer. if you die, you die. You won't even perceive the pain. if you don't die, you do your day-to-day until some sickness hits you from radiation and then die.
The fear of AI is one that does (and already has, in many cases) in fact change your day-to-day. And given how the increasing economic disparity is going, it will not be one that changes the day to day for most people for the better. No one is positive because the current societal rate of change for most people is negative.
AI is a catalyst and will only accelerate what is already happening (since it fundamentally does not create nor open up new forms of labor). So it's clear why people who feel their day-to-day will get worse are not optimistic.
> People now seems to be more negative than when atomic bomb was invented.
When the atomic bomb was invented they didn’t hand one for free to everyone, and no one had access to sending their thoughts to everyone else in world.
> Looked what happened when crane was invented
That is a terrible comparison with no useful parallels. You can’t in god faith suggest something is going to have a desired effect because something completely unrelated did too. You could just as well have compared it to asbestos.
This is why taking advice from people who 'made it' is not as smart of an idea as people seem to think it is. You are subject to extreme survivorship bias who are normally going to be optimistic. It is feels good entertainment. You are not hearing the countless voices that failed even pre-AI for small and irrational reasons.
Math is not just a "field", it's a body of beautiful knowledge. It's never been easier than before to start learning it, if one wants to appreciate it for its own sake and not as a means to get famous or boost one's own ego.
Mathematics depends on technological advances to go forward, mathematics subjects are increasingly specialized, complex and take a long time to get up to speed.
Without another breakthrough like LLM, we risked that it would simply be close to impossible to make significant progress by the time the mathematicians finish being specialized in a field.
I think two things are being conflated: whether math will continue to offer exciting opportunities, and whether it will remain fulfilling for those who love doing it today.
Grant is right about the former. But that doesn't address the latter. A field can have a bright future while losing what drew people to it.
I can relate to this. I used to code as a hobby (never professionally), but since AI came along, I've pretty much lost interest in writing code by hand. Obviously just one data point, but I can easily imagine something similar happening in fields like math.
Was farming more fulfilling before machines? In some ways, most likely: During harvest the entire village gathers and works together in beautiful landscapes, using local knowledge passed down through generations.
Preferences change. If AIs can lower some of the barriers to learn and develop mathematics that might mean more people than ever will do math.
I feel like the people you are talking about in the latter just want life to be like when they were in 8th grade. You go to school and your parents and teachers do everything for you.
Welcome to the real world, where you have to solve real problems.
Anyone following their passion for abstract thinking or whatever and doesn't enjoy being a prompter instead is degraded to an 8th grader, and even infantilized? Seriously, what a ridiculous statement to make.
I have great respect to him for all his contributions to the learners. But I think he is off on this one. While he tried to sound motivational to the folks who suddenly lost their way, he should have also advised people to explore the open doors instead of banging on the closed ones, like he does throughout the video.
Sure, math does require people in future, but it can't accommodate as many as it does today.
> Sure, math does require people in future, but it can't accommodate as many as it does today.
I actually think it probably can - after all mathematics isn't a commercially viable career and pretty much all mathematicians are scholars paid by universities and taxes. They're already fairly unnecessary and mostly kept around for interest and to have an educated population and so on. In a way they're uniquely positioned to survive the AI storm.
Not so for programmers who are almost all working for companies who would love to stop paying them given a chance.
I'd like to believe Grant but I find this assault on mathematics to be dehumanizing and demoralizing. AI has destroyed a major source of "life's meaning" for many people who pursued mathematics. Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to (and many more to boot.) Not another mathematician but an alien technology. As a scientist, I don't want to end up as a laboratory assistant to an AI. I can take not being the smartest human in the room, but I'm pretty sure I don't want to spend my life serving a silicon master.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons
I really don't understand such takes. Extend this to every problem in every profession, which seems to be both the trend and the intent (if still far off), and you vaporise the meaning from a lot of people's lives. Sure, they can find other sources of meaning - assuming having their job automated doesn't leave them constantly scrambling to make a living. This would require major social restructuring that nobody's really talking about.
Many people pursue careers based on the intersection between their interests and what society considers valuable. Being upset when what they chose to spend their lives doing either loses value or changes so much it becomes a wholey different job is understandable, and calling it "rent seeking" is very unfair, in my view.
> and you vaporise the meaning from a lot of people's lives
If the meaning of your life is to obtain a solution to a given problem, then getting the solution would "vaporize the meaning of your life" in the same way as when someone that claims his meaning of life is to raise their children would "lose all meaning of life" when they finally move out and start to successfuly live on their own. Yes, there could be some nostalgia in both cases, but if you are psychologically well-adjusted, the pros would still far outweight the cons, the happiness would outweight the sadness.
I don't think that's the same. Would you let robots raise your kids if they provably did it better than you?
These people knew someone else could solve the problem. Presumably they figured there'd still be meaningful work for them to do - exploring ramifications, new frontiers opened by the solution. Other problems, at worst. Now it all seems far from guaranteed.
I agree about well-adjustedness, but what do you propose these people do to get paid if the number of researchers with grants reduces significantly? Reskill to something that pays less, they like less, and might be automated too? Can you frankly say this wouldn't be a moral blow to anyone, well-adjustedness and all?
I don't think you can so easily call for separating them when so many people grew up in an environment that ties economic value and a respectful place in society so strongly.
> So the question remains: is it about solving the problem for humanity? Solving the problem for yourself? Or getting paid?
Say it's a mix, which I think is most likely. They enjoy the problem-solving, like doing something that feels meaningful to humanity, and obviously need to get paid. Now what?
The big assumption here is that "problems are being solved" in every field affected. Which they are not.
Just as the most basic example: software is not currently being made faster, nor performing better nor at a higher bar of quality. Maybe developers are able to report higher velocity, but this is not leading to faster shipping of software/features. In fact, people seemed to feel software is buggier than ever and companies are doubling down on it and simply adding placeholders of "AI can make mistakes". Unforgivable 10 years ago if we tried that with humans.
If anything, the rent seeking is with people reporting "being more productive than ever" and despite that less real world problems being solved than the previous decade.
> This would require major social restructuring that nobody's really talking about.
There are few concrete proposals, but a lot of people are talking about the need for it.
The reality seems to be that this will extend "to every problem in every profession" within our lifetimes. The only scenario I see where that doesn't happen is global war or other catastrophe stopping progress by essentially destroying civilization as we know it. So we are going to need to figure it out.
Many people don’t even function off this “meaning” you’re talking about. They get it from family and friends and hobbies. It’s a contrived perspective, albeit a useful and good one. But this claim of the world’s problems existing as a means to providing value to someone’s life over actually being solved is kind of an insane perspective if you ask me.
I have trouble understanding how anybody could seriously believe this.
Mathematicians are ecstatic and delighted when major problems are solved by other mathematicians. If you've followed the discussions and read the reactions, you'd know why mathematicians feel differently in this case and why more than a few are upset and feel that they've lost the thing that gave them meaning and joy.
And to put it very simply, I don't want mathematicians to exist just because I want solutions to problems. I want mathematicians to exist because I want to live in a world that has mathematicians, philosophers, writers, painters, thinkers, etc. That is a better world that makes people better.
OpenAI's proofs do not make people better. They do not enrich our lives. And OpenAI was able to produce these proofs because countless generations of human beings sowed the fields of mathematics through countless hours of labor. OpenAI is clear-cutting and sowing them with salt. Nobody should he ecstatic. Everybody should be horrified and outraged.
Let's just say that The math problem that got solved, I was working on it for many years but some company people used my knowledge my prompts and "solved" it without giving me any credits or money.
Firstly they plagiarised the books and research papers and then they plagiarised the prompts by the mathematicians.
Yes AI can make art and has caused many artists finding work difficult but AI art is always souless and worthless, same thing will be for math it will become souless and worthless because when humans who are experts in their fields invest their ingenuity then art becomes alive but if ordinary people like me will just prompt into the machine then souless things will come out that will be very worthless and disposable.
Non-mathematicians talking about this (especially in a cultural battleground like Wikipedia, yuck) will never be productive. Citing it here on HN does everyone a disservice. For those uninitiated, OpenAI used a fundamentally different method (without forcing in the Euler case) and the idea that the proof was plagiarized (other than the completely kosher strategy of using prior art, of course) is a complete fabrication.
In fact, the proof is such a mess, nobody really understands how it works. Which is becoming commomplace with these permutation machines where we can come up with something that passes some tests (e.g., a proof checker), but we have no idea wtf we did to get there, which doesn't really seem to do much to push human understanding forward.
It seems like such a dumb hill to die on, too. OpenAI literally stole the entire Internet (including copyrighted works), and we're arguing about a silly math puzzle.
The plagiarism and copyright stuff is just a smoke screen.
A lot of people are upset because they used to be special, their identities were tied to them being smarter, or having more niche domain knowledge than anyone else. Ai has changed that.
Nobody capable of a minute of honest introspection believes that. If you shuffled all the backend devs in the world and randomly assigned them a role elsewhere most will do perfectly fine. I began my own career in VFX, moved into compliance and am now working on automotive software - there's no moat around even the most niche domain knowledge, you just need to be prepared to spend time learning it. If I had to roll that into an identity it would be the learning I get to do at every turn in my career. That's what I enjoy but there's absolutely nothing unique or special about it.
Maybe the reason people are upset is simpler? Maybe people with a mortgage and kids to support don't like being told they'll absolutely 100% soon be out on their arse. Even if you don't believe that it's still tiring having to hear the same mindless taunts and vapid bullshit repeated on a daily basis.
A lot of people are upset that people are praising garbage and outright stolen output, and any attempt to disagree with this praise labels them as a luddite who will be behind on the times and is against progress.
Such a take on "people don't feel special" feels borderline bad-faith. People of science tend to be some of the most humble people as their knowledge to seek the truth constantly leaves them with more answers than questions. It's instead this borderline cult of people praising output that is understandable to them that seems to be the ones with the hubris to try and claim that thinkers will be obsolete.
According to the article you linked, there is no evidence at all showing OpenAI plagiarized Buckmaster and Alpoge. Buckmaster just speculated that since they used OpenAI's product, it's possible OpenAI looked at their conversation. Which OpenAI flatly denies.
And then your article says:
> On 13 October 2026, Scientific American published an article surveying several mathematicians stating that "the resemblance between the two groups’ methods now seems merely skin-deep."
But the AI companies didn't gatekeep knowledge. They released all their math results.
Unless you mean they're charging money for a product that contains knowledge. But that's not gatekeeping, just like selling a book isn't gatekeeping. Gatekeeping is when a group tries to prevent others from participating in a field or activity.
Selling a book quite literally is gatekeeping, since the idea is that you're prevented from engaging with the work without paying for it. Even with libraries it was society who paid for it in order for the commons to get access, but payment was nevertheless needed.
It just turns out that the Chesterton's gate is useful and people tend to think that people should be paid for their labour, since people kinda need a roof over their heads and food on their table.
It's not gatekeeping unless you're using your own esoteric definition that's different from how everyone else uses it. Words get their meaning from how they're used in the wild, and dictionaries are descriptivist, not prescriptivist. Anyone is allowed to buy the book, so it's not considered gatekeeping, even if some people may not be able to.
If you define any obstacle to an activity as gatekeeping, then literally everything can be considered gatekeeping and the term loses all meaning. Some people can't read, so offering the books for free would still exclude them. If you include an audio book, some people still can't understand the language. And both charging and not charging money for products would simultaneously be gatekeeping under that definition, since not charging places more financial burden on the producer. Not everyone can afford to print books and give them away for free.
> Gatekeeping is when a group tries to prevent others from participating in a field or activity.
And I gave a way in which charging a price does that.
I am open to the idea of being incorrect in this case, in which I apologise for misunderstanding, and concede that I'm missing the nuance but in my defence, I'm not a native speaker.
> Words get their meaning from how they're used in the wild, and dictionaries are descriptivist, not prescriptivist.
But I didn't explain that clearly. What I mean is that definitions are always imprecise because language is imprecise and dictionaries (or people) try to keep definitions reasonably short and simple. Dictionaries are trying to describe what the words really mean in the wild. They aren't the source of that meaning.
For example, if we look up Merriam-Webster's definition of "game (noun)", none of the definitions really work for a game like Solitaire without also including an activity like reading a book.
The two relevant definitions are
1. a physical or mental competition conducted according to rules with the participants in direct opposition to each other
2. activity engaged in for diversion or amusement
(there are a bunch of other definitions as well, like animals you hunt)
The second definition is too broad and the first clearly excludes Solitaire. If you were deciding what a game is based on the dictionary definitions, you'd either think watching TV is a game, or that Solitaire isn't. But that's not the case.
Charging money for products isn't considered gatekeeping. So from a descriptivist perspective, it isn't, even if it seems like it should be, because the word isn't used like that. Banning a group of people from an activity is gatekeeping. If mathematicians said only mathematicians can prove theorems and correct proofs from non-mathematicians won't be accepted, that would be gatekeeping. But they don't do that.
If you want to use a broad definition of gatekeeping that includes virtually all human activity, then the response to any accusation of gatekeeping could be "well, everything is gatekeeping". That road just leads to pointless and confusing conversations.
If we play a game of chess and I move the pieces to the final position on the first move and declare victory you might feel that something was missing, even if I'm right.
This is not quite like that but the feeling I get from it is much the same. Mathematicians are first and foremost busy with understanding math, not with 'solving' math though they are solving individual problems within the domain of math. The journey towards that understanding requires specialization and often lots of studying.
To quote Douglas Adams: "If 'metal nose' here is going to give you God's phone number then the philosophical question of whether there is a God becomes meaningless."
It is the journey and the questions that matter as much or more than the answer does.
And with math being a branch of natural philosophy I can see why they would be a tad upset at this shortcut because it strips the collective efforts of a large number of people of their prestige and feeling of time well spent. Imagine your life's work reduced to a short string of bits, and worse, that short string of bits was created by a machine that effectively is still a toddler.
> It is the journey and the questions that matter as much or more than the answer does.
Selfishly, as someone who enjoys programming, I feel the same way about the journey. But let's face it: for everyone else, the outcome is what actually matters. Mathematicians argue that their journey may lead to novel insights, but are those insights really valuable? Are they going to help the LLMs solve more problems? And are we sure that the LLMs can't deliver those same insights?
I think that ties in with the 'who will train the juniors' angle: if the ladder consists of nothing but the top rung because the AI combine stripped away the rest of them then a lot of fields will be looking at zero new entrants. Nobody wants to compete with a machine for their living and sense of self value. I know I don't, and obviously I can't speak for anybody else but society has pretty much programmed people to tie a good chunk of their identity, success in life and general well being to their skills and ability to put bread on the table. You can't just toss that in the bin for 3/4 of the current crop of professionals (I'm seeing the mathematicians as simply the first (and probably not even the first) of many).
I don't know if you have kids or not but I have two kids in high school and keeping them motivated through the AI revolution is a serious challenge and some of their classmates have already all but given up. The next generation down the line is going to grow up with the same kind of attitude towards thinking that you might have towards the skill of map reading. And I think we'll all be poorer because of that, not richer.
Exactly. As a software developer, AI has given me more time to tackle higher-order problems. The actual architecture, optimisation, and user experience.
Mathematicians could:
- Continue working on philosophical aspects of the solution and not bothered by whether the solution is known or not. It is not a movie that gets spoiled when the ending is known.
- Or better, demand from AI labs, how they would like to see AI helping them on philosophical aspects.
…except the machine will be better at these aspects too :D
I find it funny when people suggest "just re-orient from knowledge work X to knowledge work Y, doh!". Not realizing all knowledge work is on the chopping blocks.
This misunderstands mathematics. There are entire branches of the subject that have no practical use. Some things also appeared to be useless for centuries before physicists discovered they actually have an application.
> It is the journey and the questions that matter as much or more than the answer does.
That only makes sense to me when its what someone chooses to spend their time doing. When they expect someone else to pay them for it, its the end result that matters.
Maybe its a fundamental flaw in capitalism or money itself, but we can't expect to be paid for the sheer love of the game. Others will only end up paying us if the expected output is worth it.
Well we have been paying people for the pure pursuit of knowledge for its own sake since the scientific revolution, which is kind of the material base for capitalism, so I don’t think your argument holds much water. Why knowledge and following curiosity facilities general prosperity is maybe an open question but that it does is inarguable.
Capitalism incentivises paying people to pursue more capital, not the putsuit of knowledge.
And to be clear I don't say that as a good thing, it may be a flaw in capitalism, but we don't psy people simply to chase knowledge for the sake of the chase.
On one hand I agree. I’d also add that there will be no end of math problems to solve. That some were solved will only lead to new ones.
That said, I think what has mathematicians… upset is probably two things:
1. These are hard problems. Hard enough that solving one could take decades of work. And there’s tons of collaboration involved. Pivoting to another - and making progress - isn’t exactly something you wake up tomorrow and start doing.
2. I think motivations matter to some. And the AI companies doing this aren’t doing it for the betterment of math or even society. They are in an arms race to prove their product is superior and any careers that are damaged collaterally be dammed.
Why should we be estatic that some signifigant math problem was solved by machine rather of a human being in a language only the machine understands? Don't you know that problem was solved by a space alien a million light-years away a long time ago in a galaxy far far away? Makes no difference from the meatbag perspective: both claims are untestifiable.
In fact you should be estatic that in a paralell universe all math problems have been solved, so there's no reason to pursue math at all (we did it reddit!).
When your job is automated and you're living in the streets, just remember that you should be estatic that the job is finally being done more efficiently by a robot. Like, we did it. We finally did the job right. The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system that exists for... what exactly? What is the end goal of all of this? Who does the system serve in an economy of no consumers? What is the point of solving niche mathematical problems if no living person can comprehend the solution?
> The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system
There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
To these people, it sounds like a cruel joke that people get paid 3x their salary, and after AI can do their job we learn that apparently the only purpose of their was their own self-actualization.
I don't actually believe that about math, but that's what a lot of people in this thread sound like.
I thought technology was supposed to liberate us from the fields, but it turns out that's what wealth is for, and the wealthy want us back in the fields (no more escape through special training or skill).
Why would the wealthy want you back in the fields?
You were useful in the fields to the degree that was necessary for food production (sustain and grow population) and for wars (using said population to expand and extract more resources).
Once machines automate material comforts and exertion of violence (already have, to a large degree), humans become a pure loss center. Why bother with "fields" lol.
Because fundamentally: certain humans desire power to rule over other humans. Even if the fields (metaphorical or literal) can be done more efficiently by robots, they desire that power to exert over others.
So they will keep some ready for those tasks simply to fuel that irrational desire. They will instead use the more efficient bots to enforce work on the fields rather than work the fields themselves. Or perhaps we go full Matrix and find uses for humans that robots can't properly replicate.
>There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
I know, I have that job! And I enjoy it. But the robots are coming for me too.
A bit sad other knowledge workers feel that. I know my job isn't anything trying to better humanity; I just make video games. But making those games (or rather, the tools to make those games) has an end result to have people enjoy themselves a bit in a decreasingly enjoyable world. So there's my fulfillment.
But I understand it from a blue collar perspective. I tinker at toys in a metaphorical basement and I live a cushier life than many who give their bodies to their duty. That doesn't feel fair at all. But I mostly wish that was motivation to band together and get blue collars paid better rather than cause this inter-class divide while the capitalists ransack all of society.
We’ll put IMO. This expresses well the way I’ve been thinking about “the mathpocalypse”.
I feel sad and even a bit forlorn when I think of jobs that provide purpose, meaning, motivation, and satisfaction (not to mention $$) to human beings being lost to servers in racks and soulless machines. I think many people feel similarly.
However, I do believe that when a couple problems get solved that massively benefit all of humanity — e.g. a massive cancer breakthrough, etc — a tipping point will be reached and public opinion will reverse and enthusiastically embrace AI, and will accept not only diminished personal meaning but outright technocratic rule. This would be a huge mistake, but I really believe it would happen.
And as we know, solving interesting math problems is a leading indicator of big practical results to come.
>However, I do believe that when a couple problems get solved that massively benefit all of humanity — e.g. a massive cancer breakthrough, etc — a tipping point will be reached and public opinion will reverse and enthusiastically embrace AI, and will accept not only diminished personal meaning but outright technocratic rule.
Is solving cancer worth ceding human meaning and human autonomy to the machines? I haven't seen anyone ask this question but it seems the central issue of this revolution. Personally, I don't think it is.
Perhaps machines will lead to a perfectly homogenous society completely absent of negative valence whatsoever. But if every experience is also devoid of any personal meaning, what's the point? The optimal human state is not one of peak hedonism, or wholly absent of suffering.
> Is solving cancer worth ceding human meaning and human autonomy to the machines? I haven't seen anyone ask this question but it seems the central issue of this revolution. Personally, I don't think it is.
Solving cancer alone? Perhaps not.. Unless you have cancer.. Solving all diseases and aging? Well... I would rather be alive and live like an AI's housecat than dead and free. And I suspect that many people who publicly disagree are just performative, and would actually make the same choice when push comes to shove, and they have to actually choose between "diminishing their autonomy to the machines" and imminent death.
The Christian influence on the world has been undeniably positive. Seeing death and suffering as the enemy and organizing society around minimizing it has been a boon to human progress. But now we come to the dark side of this view. A fear of death so complete that we are willing to sacrifice everything of value to prevent it. Our society has become so divorced from our natural state that death is seen less as an inevitable part of life, and more as a corporeal enemy that must be resisted at all costs. As it turns out, too much of a good thing, whatever it is, leads to absurdities and atrocities.
No, I do not think human autonomy should be sacrificed to defeat death. I personally do not fear death. It's as irrational to fear as it is to fear a deep sleep. I do fear dying painfully. Tragically, we as a society resist alleviating the pain associated with the process of dying (by speeding it up) for the same reasons. If only we could learn to take our principles in moderate doses.
> death and suffering as the enemy and organizing society around minimizing it
> A fear of death so complete that we are willing to sacrifice everything of value to prevent it.
> a corporeal enemy that must be resisted
I am afraid that you know nothing about Christianity. The beliefs and values you describe are antithetical to the Christian life and our worldview. If you've ever just examined the life of St. Teresa of Calcutta, you'd understand how absurd it would be for her to "fear death" or "minimize suffering".
We seek to follow, and imitate, Christ Jesus in his life of suffering, his death and resurrection. We do not resist, or minimize, or fear any of this. To do so, would be quite heretical to us as Christians.
Of all times of the year to bring this up. All Saints Day, celebrating the eternal life of those, named and unnamed, who have preceded us in death. All Souls Day, to pray for all the departed souls who suffer in Purgatory, after death but before their Heavenly reward.
I don't know what religion you are trying to describe, but to me it sounds like atheistic secularism. It is atheism that fears death, and utilitarianism that seeks to minimize suffering. Not Christians. Goodness, gracious.
To understand my point one must separate the metaphysics from the practical effects of the belief system. Christianity represented a step-change towards humanism. This must be considered in the in the era it was founded and compared to the competing ideologies at the time, i.e. paganism and its various death cults. Christianity institutionalized ideals like equality of men, the sanctity of life, charity, self sacrifice, etc. These ideals are the precursors to civilization.
The particular ideology of Christianity was super effective at laying the groundwork for modern civilization. Of course, these ideals have since evolved and have since become some kind of secular ideology. Granted, it was imprecise to attribute a fear of death to Christianity. But the sanctity of life is in practice a close cousin of a fear of death. Modern secularism having no metaphysical alternative has made this fear explicit.
You shouldn't. Maybe you should learn Hilbert Calculus so you can appreciate it.
It's like asking if what someone wrote a beautiful poem but it's in japanese. Maybe hearing about it motivates me to learn japanese, or maybe it doesn't. But as a non-speaker it makes little impression on me.
There is a difference between the process of solving a problem and a problem being solved. If I solve a problem myself, I understand it, I find out something new, I get to try lots of things. It's engaging and fun. If I tell you to go solve a problem, I can learn it afterwards but I miss out on the entire process.
Personally, I enjoy the process of solving problems. I do not enjoy wrangling unpredictable AI agents.
For a personal experience I 100% agree. Where I'm not sure where I land is when the problem solving is a job people are paid for. I wouldn't expect someone to be paid to enjoy the process of solving a problem, I'd pay them to solve it.
There are plenty of things I enjoy doing, but I try to do them as often as I can for the love of it rather than because someone is paying me to enjoy the process.
Previously there was no way to pay someone to solve a problem without someone going through the process of solving it. I think what people are upset about is that any kind of problem solving is no longer a stable career path. Even the skills replacing the problem solving jobs are liable to disappear as the interfaces are refined and models improve.
You never hired someone to find something useful to improve or fix? There a lot of people who are really good at that and really bad at just doing the things you tell them to do.
I've never hired anyone only to enjoy the process of trying to solve a problem. Imagine hiring a plumber that never solves your plumbing problem but had a hell of a time enjoying the process of trying to understand it. Would you want to pay them for that?
This is pure math research we're talking about here. It's not exactly lucrative and people looking for commercially applicable results ASAP weren't funding it anyway.
It sounds like your argument is effectively that it isn't an economically viable pursuit.
People have been getting paid for it, and hopefully that can continue if they enjoy it, but why should we want them to be paid only to chase theoretical math if it has no valuable output, or if the value is in the pursuit rather than the output?
My point is that this was already the case, i.e. math research was already not a "dollars go in, useful proofs come out" field. The people lamenting the future of mathematics are largely not focused on the economics, they're focused on the fact that anything they might apply their efforts to could get sniped by a frontier lab at any moment. That is obviously demotivating.
But reading the threads here on HN, in response to people saying "this sucks", AI boosters would rather redirect the conversation into economics and feign outrage that people are being paid to do mathematics at all.
Suddenly folks seem to be both in contempt of the idea of solving abstract puzzles without practical application, and certain that they want a higher efficiency of abstract puzzles solved per dollar (again, puzzles they probably don't care about).
The ideal human society is not one where people are narrowly focused on creating widgets or increasing efficiency, narrowly construed. An ideal human society includes intellectual pursuits. Some of these pursuits do not suit dabblers, they take deep expertise that can only happen from a lifetime of directed effort. We are collectively better off when some value is spent in ways that isn't aimed at maximum efficient allocation.
It's funny, the justification for accelerationism is that people can be paid (UBI) to pursue their passions. On the other hand, we have those that are asking why anyone should be paid for work that isn't economically viable. I suspect we're being sold a load of bullshit.
I don't support a UBI, for what its worth. The idea is nonsensic from my vantage point, if there's a certain minimum level of good people should have access to it makes more sense to give it to them rather than to give them some level of cash that can on theory buy it.
More importantly, I'm curious how you define an ideal human society. How do you land on what ideal is, or what it would take to get there?
>More importantly, I'm curious how you define an ideal human society. How do you land on what ideal is, or what it would take to get there?
The question is in what context does the human psyche thrive? We find meaning in personal struggle and overcoming obstacles. We're happiest when we're striving for something out of reach but seemingly attainable. We're much less happy when we have all of our needs met but have no source of meaning or fulfilling struggle. Our evolutionary history is one of struggling against hardship and finding personal meaning in the process. This is a core feature of our psyche and it is to our detriment to eliminate it.
This isn't to say we should all be struggling for our next meal. Much like cats, our core drives can be exercised and satiated through a simulacrum. There are many ways it can be satisfied, but strive we must, against something with inherent meaning to us. The problem with AI fully realized is that it takes away most avenues for human achievement, thus the struggle loses all meaning.
It seems like everyone presumes that the currently proofs which are difficult to parse will stay that way. LLMs are really good with language. There's no reason that the next wave of proofs won't be accompanied by very literate explanations that mathematicians can generate understanding from.
One real limitation is context size. 1M tokens is enough to do a lot, but the Lean graphs they are making are way too big to fit, so an LLM will never have the complete picture.
Nope. That's why a lot of knowledge comes down to compressing large concepts into chunks we can understand from new ideas and concepts. LLM's don't tend to be very good and synthesizing such concepts.
I’m seeing this perspective expressed a lot lately, but (so far) only online.
Understand that there’s more than one way to prove something, that there’s an art to making something understandable, and that humans tend to take the most understandable paths (to humans.)
Models often don’t do that. But in solving, or claiming to solve, important problems, they nevertheless remove a lot of the excitement and incentive towards working towards a solution humans would naturally find. Plus, a lot of these problems really don’t have any critical applications at the moment. They’re done for the love of the game.
Does that bother you? That your tax dollars pay people who do math out of curiosity?
The primary value of math has never been about producing "solved problems" (is there any practical value in "solving" NS in itself?). The primary value of mathematics has always been about "machinery for thought", i.e. the abstractiosn and methods that produced the solution.
I think there is a little too much pessimism of the "math is dead" sort. As long as there is a need for humans to think there will be value in doing math.
Mathematicians usually care nothing about application of their work. Working on interesting problems is their only motivation. Practical applications are almost always happy accidents.
This goes back to the hope that robots would do the laundry and the dishes and the cleaning up so we could write and play music, create art, and solve mathematical problems.
Instead the AIs are doing all of that leaving humans with only the dishes and the laundry and the cleaning up.
Whatever doesnt count as maths is just not maths. Its just carrying out instructions to get some "gain".
Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.
And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.
This goes back to the classic story for "kids" about the emperor that has no clothes.
As of this comment you have 26 comments out of 206 total on this comment section, more than 10% basically all spreading FUD to try and make other people as miserable and pessimistic as you. I'm not sure what your motivations are but I'm glad we have people like Grant on the other side trying to keep a positive outlook on life and the future, and I hope all you eternal doomers who constantly try to bring others down with you find joy as well.
If math is nothing but solving puzzles for fun then I think a lot of people should be very pissed off that they are doing hard labor while being taxed to fund a puzzle hobby group.
Of course I don't believe that math is just fun puzzles. But if it were, then it would deserve to die as a career, AI or not.
A lot of people went into maths because they liked not only the results but the process of research and discovery. That has been taken from them. No matter how you feel about AI, I think we should all pause and at least think about this and validate those feelings.
Look at the most upvoted comment on that thread:
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I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
No, I think it's just super cool. One of the things I hate about it is that you can't really explain what you find cool about it; others just have to see for themselves (in some sense it's like a self-induced trip to sit there and work out analysis/topology proofs in your mind's eye, visualizing little nested blobs doing their things), which of course nearly no one you will ever meet has any interest in doing. I wish more people wanted to talk math/physics with me lol.
I just want to know more. There are infinite rabbit holes. Like in uni and for years after, I wanted to know why convolution should be so important. Was I disappointed that someone else had already figured that out (that it's what you get when you form the vector space over a group and define multiplication as group multiplication) long before I was born? No way! I was stoked to finally have a satisfying answer! I wish they'd find a way to stuff that into applied analysis for engineers because it's cool and engineers should get to see cool math.
But then I went into software (partly because it was a hobby of mine anyway, and partly because it pays well), and learned a long time ago to leave any notion of artisanship or nerd crap at home. Java programmers spent forever arguing against type inference, Python/Ruby programmers think static types are a hindrance, and Go programmers spent a decade saying generics make things more complicated. Metaprogramming is generally synonymous with "too clever." It's cool that the relationship C^(A+B) = C^A C^B (or generalizations) says that the way you handle an enum type is to pattern match/provide a handler for each constructor, but I'm not going to burden my coworkers with that nonsense.
AIs are currently reducing human knowledge and cognitive capabilities, replacing it with machine capabilities instead.
It’s going to destroy both academic funding for people wanting to learn more through research and salaries for people currently doing cognitive work in corporations and an irresistible crutch for students using AI to do their work for them.
It will probably reduce most people's cognitive capabilities, but most people aren't interested in learning. If you don't want that for yourself though, it's great. You now have your own personal professor available 24/7 to answer questions about whatever topic you're learning. Take a picture of a page with your phone and ask it something you're confused about, or to check your understanding. Get immediate feedback. It's awesome.
Similarly, at work, it's never been easier to have data to make decisions with. Or to just try stuff out. Really great. Gets rid of what would otherwise be massive amounts of tedious "thinking" that drains your brain but isn't actually challenging in any way.
It's early yet to see what effect it will have on research. Experimental science is full of interesting, cognitively engaging topics as well though. Or maybe they end up like me and do boring engineering work for pay, and read cool stuff that the AI has figured out in their free time. It's not all that bad.
I think it might be a result of shock to believe it’s been taken away - you have my sympathies.
Mathematicians got a new toy. It’s up to them to pick it up, play with it, and figure out what it can and cannot do.
While I cannot guarantee it will stay this way indefinitely, there is still plenty that AI cannot do that humans still can, and asking the right series of questions remains an art of its own. There is still plenty of original work to be done.
As Arnold Schoenberg stated in the 20th century, “there is still plenty of good music to be written in C major.” The search space is vast and today human judgement is still required to really navigate it usefully. No LLM has yet written anything like Shakespeare that has superseded Shakespeare in any culturally meaningful way. Although programming is supposedly just about solved, I expect to see numerous billion-dollar startups emerge over the coming decade, rather than all of the innovation running out at the speed of tokens.
“ if you're mad about your problem being solved, maybe you weren't in it for the right reasons”, politicians/financial advisors/military members/etc… would like a word with you.
What, in your opinion, is the point in solving these problems if no human is there to witness it? This is like suggesting we have AI watch movies for us and read its summary afterwards. In fact, why do anything anymore?
Yes, much of pure mathematics is "playing with puzzles" to the end of the joy and beauty revealed by a human solving them.
I suggest listening to "Math Vs Machine" [1], which has a much more nuanced take. It clearly lays out two types of use of AI in math, one that helps humans have better understanding, and one just bulldozes problems without helping us get any insights. It also touches on the topic of "does it matter if the machine does things in ways humans cannot understand".
Mathematicians are saying the current papers are pretty inscrutable and use terminology unfamiliar in the math sub fields in which the models are generating proofs.
Cause it looks like it's mining one subfield for a pattern and applying it to another. (The take from the few math folks I know who have looked into items of their interest).
Computing has the same issue. If we swapped a PLC programer with your average SV software engineer for a week both of them would have a really bad time.
I'm not entirely sure this is fair. My belief is that mathematics exists in the intersection between art and science. I don't believe in progress for its own sake, so I'm inclined to say those interested should undertake it for the art, or to "play with puzzles." The rent-seeking argument and "weren't in it for the right reasons" is the same argument as calling musicians sellouts when they start making money. Making money doesn't make you a sellout, but it can.
Mathematics is more akin to art or a sport to many — philosophy, too. I don’t see that as a bad thing.
But there’s always a risk that someone in an adjacent domain makes a breakthrough that completely reshapes the research landscape overnight. It’s happened before AI and it will happen at some point again in years to come. Grief is understandable, but this isn’t the first time or the last time.
Only those that aren't in a field and see its existence justified for purely instrumental reasons can think its value is merely in its practical output. Personal meaning and fulfillment come in many forms. For mathematicians, part of that value is through solving problems, but it's also partly about the struggle itself, gaining understanding, expanding the frontier of human achievement, being a part of a community that values these things, playing a valuable role in the progress of humankind and making a career out of it. Having all that swept away overnight will lead to an existential crisis for anyone who is on the wrong end of this process.
It's quite bizarre how many people feel so personally affronted at the existence of a rather exclusive intellectual community that they take glee in seeing it decimated overnight. But make no mistake, AI is coming for the things you value as well.
> If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
I'm not a mathematician but I find this framing to be rather non-pragmatic and frankly, pointed.
In the process of Leonhard Euler's "rent-seeking" so he could "play with" bridge crossings he invented a completely new branch of mathematics that is the basis for things like Google Maps today. The process of working with these problems is just as important if not more, than just solving them.
Many people don't seem to understand that pure mathematics is not a practical applied science, nor is it in the business of inventing things.
Pure maths is much closer to philosophy or art than practical problem solving. Yes, we're extremely lucky that mathematics also happens to be a fantastic formalism for solving practical and scientific problems, by the practical problems are not remotely the subject matter of pure math. Of course, many mathematicians did advance theory in order to solve specific practical problems, but the pursuit of theory for theory's sake is also an important human activity.
Historically, this freedom from practicality has been important. It allows mathematicians to explore purely theoretical issues that have no practical bearing today but that might well have relevance in the future. We don't know. Carving out dedicated resources in society for that activity, though, has proven very beneficial for other sciences.
You have no computer, you have no neural nets, you have no AI, without at least some results from pure maths. Maybe keep that in mind before you crap on mathematics for its lack of immediate practicality. Not all good things in life arise as solutions to concrete and immediate material problems.
I wonder how many math professors think they were actively working on well-known unsolved problems. Is it just a small elite club, or is it every tenured / tenure-track professor in all R1 schools?
This is an awful and really ignorant take. The manner in which the problem is “solved” matters a lot, and these AI solutions are about as poorly-done as possible. That a solution exists closes the door on almost any sort of support for finding another, better one, which is the real problem. If this continues, we wind up with a field with no open problems, no practicing mathematicians, no future mathematicians, and no way to come up with new problems (this latter being much more important than solving existing ones, in the main).
AI wouldn't advance the state of the art? It promises to do it at an incredible rate.
What you are complaining about is not that the state of the art wouldn't be advanced, but that vanity would not be served. Vanity (as part of Pride) is one of the seven deadly sins for a reason, and Pride has been described as the root sin, the worst of the lot, since all others stem from it.
It's completely natural to be attached to the process of your job, rather than the outcome. It's not a phenomenon restricted to mathematics. We can say it shouldn't be like that, but it is.
What? Why are we nullifying so many human factors in one stroke? Humans strive to contribute to their community and to be recognized for it. We aren't machines, we have social and financial needs, and enjoy competition. Math being solved would mean part of humanity losing these parts of their lives.
Would sports teams have as many fans who enjoy their games, if all the humans were replaced by robots? Your team may win, so I'm sure you'll be happy with the outcome, but maybe something got lost?
I for one have always felt inspired when reading about remarkable human achievements. To think that those might be coming to an end, replaced by AI, takes the humanity out of those stories.
How is your argument any different from the classic Luddite argument? Why is doing math different than making textiles? Why does math deserve special protections when other types of workers do not?
There will be human achievement no matter how much automation and robotics we have. There’s an entire universe to explore and colonize. Plus people still want to see other people do things like perform music or play sports.
Well sure, but people do still want to watch videos like 3blue1brown in-depth explanations, and they do still want to learn math for its own sake. People can still do math and derive enjoyment from it.
Incredibly nasty stuff to serve on the rent-seeking forum. Doubly nasty to levy at people who actually like being alive, like mathematicians. If capitalists had their way we'd all be slitting our wrists on day two of existence
I find it interesting how a mathematician enjoying theory-building or playing with ideas gets recast here as rent-seeking. It sounds much like certain right-wingers complaining that kids these days don't want to work, just stay in university studying useless things at the taxpayer's expense.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
But it could be another human that did that, and the impact would be no different.
As a software engineer this is part of my life, and always has been. I may have been working on a software product for the last 3 years, and suddenly one morning I find out that another company has released a similar product, and selling it cheaper, now the value of my work is slashed by 90%. I may even have to drop my project and find something else to work on. This is a normal part of life.
In research, there is always the same risk, that some adjacent field will completely change your field overnight due to some breakthrough.
Still, I have sympathy for the people who are grieving right now.
With the software industry, you kind of know what you’re signing up for, so you have some emotional preparation. However, this might be one of the very first truly disruptive innovations many mathematicians have ever seen in their fields in their lifetimes.
Should they have better prepared emotionally for a black swan event? I’d argue that the answer is no, but even if the answer were yes, the grief that many are experiencing is still worthy of sympathy.
I am confused why this is considered a black swan event. Does AI take the joy out of mathematics research? Yes. But universities are not laying off mathematicians just because OpenAI has released some proofs. The proofs were never the point of mathematics, it is the understanding behind the proofs, and applying that understanding to solve real world problems.
Now consider a computer science major in college who knows that he won't get a job when he graduates. Consider fresh graduates who thought they would have lucrative jobs but had to take up jobs as Uber drivers. To them AI is a black swan event. That's who I have sympathy for.
Right now mathematicians are freaking out because they think the AI will make them useless and they will have to go find real job with real usefulness.
But honestly mathematicians have been totally useless long before the first AI, so generally nothing have changed for them.
Give me an argument for not having a grim outlook given current AI trajectories paired with a political apparatus incapable of action. At least in the US.
Putin's getting old. If he dies before we hit recursive self-improvement, there's a chance some maniac gets access to the nukes and saves 4 billion of us (global nuclear war only kills about half of humanity).
> As a software engineer this is part of my life, and always has been. I may have been working on a software product for the last 3 years, and suddenly one morning I find out that another company has released a similar product, and selling it cheaper, now the value of my work is slashed by 90%. I may even have to drop my project and find something else to work on. This is a normal part of life.
The cause of what you're describing here, and the cause of the problems with AI are the same: it's capitalism, closed competition and businesses deciding what happens.
In an alternate society built around providing the best solutions for everyone, instead of being built around businesses making as much money for themselves as possible, your organisation would have been working alongside the other company to share insights into solving the same problem for everyone.
Same goes for AI: all the existential downsides of AI pretty much all depend on businesses being the main driver of who uses AI and when. If we only let individuals choose when to use AI, then they're not going to choose to automate themselves out of a job they need, or give up something they actually get personal value and joy from.
I don't get it. I have a research degree in physics, and if AI made major progress towards the big open questions (e.g. nature of dark matter) or managed to come up with a much cheaper way (or any way at all) to test a theory of quantum gravity, I'd be super happy. At the moment the research frontier in high energy physics looks pretty bleak in that it appears like the scale of construction and energies required are too high to reasonably achieve many more big breakthroughs in my lifetime. What makes mathematics so special that the entire field is distressed when their big open questions get resolved?
I think math is a craft unlike other areas of science.
Mathematics produces concepts and produces proofs of theorems. Up until now, the two things things fed into each other - you needed the concepts for the theorems and the theorems for the concepts. Now you can just prove theories without caring about the production of ideas.
Consider also, math produces the intellectual "tooling" for science in general. As I understand it, the important of grand unified comes because physics want an unified abstract conception of physical laws and thus a grand unified theory aims to be a unified mathematical understanding of the world.
I mean, as a though experiment, suppose a company produced a machine that simply predicted events in the future without giving any explanation of why. It didn't tell physicists whether any of their ideas were true or false, it simply answered question like "will this building fall down", "what will the spectrum of this star be", etc. It gave all the information of physics but discarded laws - physicists might find this a bit unsatisfying, especially if the machine was going to put them out of a job.
I'm sympathetic to the mathematicians and don't like what AI is doing. Every other profession that relies on knowledge or thinking should be watching the mathematics community as a portent of the storm to come. OpenAI has extensively thought about and planned their disruption and chose mathematics to start with for a reason - small community, verifiable to some extent, can be used to improve model training, not seen positively by many average people etc. The AI companies are going to come for every field one by one.
I've never quite understood this sense of meaning. The goal could never have been to see these problems solved or to further understand how the universe may work. The goal was the chase itself, or the sense of pride for being the one to crack the answer.
Also its worth noting this technology isn't alien. I don't personally want us to invent AI, AGI, ASI, etc but they aren't alien - humans are very much making the choice to invent these things here on earth.
That's not what people mean by alien. It means that we can't rely on human intuition to predict how they will behave. Their intelligence is not like ours.
I as a non maths person am not sure what you mean. Isn't AI solving lots of problems advancing the field? I understand that that maybe demoralising, but otherwise what do you mean by "assault on mathmematics"?
Solving problems and advancing the field are two related but separate endeavors.
Nobody has solved the Riemann Hypothesis, but it has been highly fertile ground for new mathematics. Answering the question is of far less value than the question itself.
1. One view of the field treats Maths as directly solving real-world problems. Under that lens, yes, solving problems is directly advantageous for the field. Even so, it's not necessarily a good thing for the participants. Suppose the incentive structures require tackling hard, long problems, the field attracts people who enjoy that sort of thing, it's hard a-priori to tell a hard problem from an aggrandized brute-force proof search, etc. Even if directly producing proofs is the desired output for the field, a capricious machine occasionally solving 40% of the big problems the field is working on is still demoralizing. On a human level, if a society has organized around producing 100yr+ problems and bestowed on you the privilege of tackling a few of them having the last 40yrs of your work solved by a fancy calculator is never going to feel good. Sure, that means that in retrospect that was a problem we could have waited to devote human effort toward, but you couldn't possibly have known that at the time. You worked hard, made locally correct decisions, and later found out that the work was worthless. Beyond that, I haven't seen any model of "Maths 2.0" produced where that issue goes away. We still want people to devote their lives to hard problems. The machine will still advance and solve a moderate fraction of them at random, killing many of the field's life's work. What motivation do you have in that environment to pursue those challenges in the first place? Why not pursue adtech or fintech and make the world a worse place instead? Solving 40% of the problems isn't +40% throughput; it's -60% as the rest of the field leaves for greener pastures, -inf when nobody's around to construct the right problems in the future..
2. "Solving problems" isn't directly the point of most of the field. That's true both from the perspective of most problems requiring many intermediate results (solving one useful thing requires solving many less useful things) and from the perspective of building the machinery capable of solving problems being much more important than the solutions themselves (a properly presented proof leveraging clever, new techniques is infinitely more valuable than whichever thing it proved -- indeed, the Millennium Prize problems were chosen precisely because it was assumed they would create such techniques, and for the human-solved ones they did -- without new techniques, eventually the field caps out at whichever frontier of knowledge we're currently stuck at).
3. A third view of the field treats it more like art. A machine producing behind your back the painting you were envisioning, or at least a close enough simile to fool the masses, doesn't advance "art" in any meaningful sense. It's extremely demoralizing when flaky cast tools are passed off for proper forged variants (your work is better, and it's sad to see people choosing a wrench they'll later snap in half instead), and when at a creative level people are accepting mediocrity instead of something objectively better.
So there's an interesting question about what mathematics is that the AI solution space is driving a wedge into and cracking wide, where previously the cracks were visible but could be ignored.
When is a problem in mathematics "solved?"
There's an old joke in math and computer science about a huge leap of logic in a proof either being flagged as "left as an exercise for the reader" or "trivially shown." The problem being that things are only trivial if you have all the context to know why they're trivial.
We can claim a problem is solved if there is one paper explaining the solution with airtight logic that is understood by five people on the planet. And that is the kind of solution that LLMs can kick out (by basically, to hand wave a lot of details that I will admit to not fully understanding, doing a search across the whole problem domain with vastly more capacity than most human beings to do the symbolic manipulation that makes up the mechanics of mathematics). But what does that really mean? To have something "proven," but only to the comprehension of five people on the planet?
3blue1brown is making the interesting argument that perhaps mathematics practice shifts from a frontier that AI might actually be better at exploring than humans, to the process of digesting the output of that exploration and making it sensible and comprehensible to the billions of mines that could take advantage of that knowledge... If it were shaped in a way that could stick in their brains.
That's a kind of creativity that AI is not likely to be good at in the near future, because AI doesn't really "understand people."
That's literally the 7.3k Upvoted top comment and I also think Grant didn't chew this one through appropriately.
I was kinda offended at 17:10, where OpenAI paper dumping proofs "takes all the wind of [mathematicians] sails". But it's so much more than that.
He did go more into it at 30:00, where he accepts that something is lost here. Or as Terence Tao said, the "age of heroes" in mathematics is has come to an end. I think Grant's points on funding and maths having a strong future are true. But I still think the dehumanizing part wasn't properly honored. But then again, this is supposed to be positive push into the future, so dwelling on it is not something Grant wanted to do.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
That seems like a glass is half empty attitude.
For one, the problem is solved. You should be glad. That's what you wanted...
Typically every solved problem opens more doors than it shuts.
We're pretty far from knowing it all.
It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
Now you can use AI to help you.
Sure, if you refuse to use it, then you're screwed. That's a you choice. Not inevitable.
The only things in life that are certain is change and death.
Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
The glass is a whole lot less than half empty. The pessimistic attitude is a rational response to our environment.
The only way change this situation so that it comes out positive is to enjoy being a slave, but hey thats a you choice.
>Typically every solved problem opens more doors than it shuts.
>We're pretty far from knowing it all.
Open doors to whom? AI or mankind? We have never been farther from knowing it all. The information knowable by people will become a sliver of the total relevant information in the world.
>It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
In that instance, the busywork was automated and challenging work remained. What we are talking about here is the reverse. It's the automation of all of the cerebral thinking.
Imagine that all of the cerebral and beautiful aspects of math were automated first, but for some reason humans were required to specialize into number crunching instead. Now open your eyes.
>Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
The thing about amish people is that they own their own land and grow their own food and are independent within a governmental system that respects their property rights. The rest of us renters and feeders operate within industrial society-work or die.
The disposition amish people have towards technology has been ahead of the curve.
>You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
I would also encourage my peers to enjoy what little time they have left. What we are witnessing is the end of history, and I am honored to experience it. However I get the impression your nature is to go out with a wimper.
The whole point of current AI is to replace ALL human contributions, in every field. Collaborating with humans is not a consideration, as shown by OpenAI leaving practicing mathematicians completely out of their process.
> math has destroyed a major source of “life’s meaning”
YOU ARE NOT YOUR WORK! My god people! The meaning you get from life shouldn’t be reduced entirely to the job you do. Mathematician, or programmer, or pilot, or ship captain, or janitor or otherwise.
I already had to learn this, but the sooner you decouple your professional life from “what makes you… you” the better.
A lot of people derive their worth from something external. AI brings the emptiness of that worth into sharp relief, but it was always empty. It used to be easier to ignore, though.
The obvious retort is "that's cold comfort to people losing their livelihoods!" But that's not the discussion, and (at least at this point) we're not at risk of mathematicians going hungry. It is obvious that AI will have a profound impact on what mathematicians do. It is not obvious that we won't need them anymore.
I'm not sure that's a fair summary of the situation though. If the machines understand math but humans don't, we're going to be in a bad bad bad spot.
We need humans to help guide all this, need to learn all we can.
I agree with Sanderson that the opportunity seems larger than in the past. The challenges are quite different, but if somebody loves math, loves learning about it, like I do, I see so much opportunity.
There's going to be so many more connections to evaluate, so much work needed for unification and simplification and pedagogy, and above all there's going to be intense demand for mathematical taste.
Well that's the point, there's immense value for human involvement in these skills. More now than in the past. If you can do more with math, additional funding avenues open up.
Jane Street will be using tons of AI in math, but boy are they going to need a lot of humans to try to keep it all under control.
Agency and control, the most important. Even if LLMs could somehow assimilate all the knowledge that's not available in their training datasets that's essential to all aspects of our current economy, which they can't they don't know human desires.
Doesn't bode well for all of us meatbags, actually. AI might now be better mathematicians (if that's even true for now). But if progress continues, it might be a better <your job here>, and even worse, wife, husband, parents. Black mirror territory.
Another pop culture reference: in the first book of the "The Three-Body Problem" trilogy by Liux Cixin, physicists get depressed by having their field of work blocked.
Pretty much the inverse situation, but also the same situation - having your field of expertise completely disrupted. Anyone would be troubled.
Back when CAD programs were going mainstream in companies in the 70's and 80's, civil/elec/mech engineers were in an uproar because they thought that CAD was going to replace engineers.
What ended up happening was that draftmen became a profession.
Not saying that we stick our heads in the sand and say AI will just generate jobs, because the cost there will most likely outweigh the benefits in the grand scheme, but there is definitely a world where mathematicians hand down direction to grad students utilizing such tools for research or some other framework that just doesn't resemble what we think of today.
It is not the same comparison. CAD produces exact same drawings as handwritten ones. It purely makes engineers more effective. It just took the menial side of the work. You still had to care about every single detail and tolerance. You still followed the same way of manufacturing things. You still do the smallest parts of it. Just like word processing vs handwriting a book / letter. You still have to type every single letter. You still think every sentence.
AI is the complete opposite. It takes away the thinking part. When people use AI, they tend to offload a lot of thinking part to it as well. I use it because company policy. But if you care about every single if case and every single variable name, writing by hand is faster unlike CAD.
History repeats itself. Now it’s the moment of weaving machines. AI is the new weaving machine. It needs couple guys for the maintenance. The other 198 guys were freed from the hard work. It’s not the CAD moment.
Before the industrial revolution weavers worked from home in a relatively peaceful environment, set their own hours, and made a respectable living.
After the industrial revolution they worked 14 hour days in a thunderously loud textile mill, so full of airborne lint that you could hardly see. The pace of their work was set by machine, which frequently caused serious injuries, and their wages often weren't enough to live on.
At the time of Munich Olympics German workers did occasionally electronics assembly at home. Or some electromechanical components like switches, relays, cabling, you name it. Pay per piece, not hourly rate. Simple hardware in today’s terms with generous pay. Later it was automated and today completely outsourced. Cycle seen in so many industries.
I can repeat myself: history repeats often enough.
You'll be surprised to learn that the opposite is true today (as of 2015 when I last worked in a licensed engineer capacity). CAD has near eliminated draftsmen, similar to how automated testing has eliminated QA. Engineers are performing all of analysis, design and drafting today. Similar to how programmers are responsible for testing.
How is that any different than another kind of automation?
AI will make mathematics so much more approachable, comprehensible, and applicable as more problems gets solved. If the costs is a handful of PhDs tenure track, so be it. Academics didn’t much to seem to mind when that happens to blue collar workers.
Nothing stopping anyone from studying mathematics here.
I keep hearing these “AI will make this” and “AI will become that”. Boosters are always making these claims for years now, but whenever AI becomes more powerful everything just sucks more.
I don’t buy these claims anymore, and haven‘t been for a long time. I think you [as in you boosters; not you specifically] are full of shit. I don‘t think you know what AI will become, you just dream up some scenario where everything becomes better by some magic, but it won’t. It will become worse. People loose their jobs, people loose their tenures, and instead we get just more and more slop, more and more span, energy becomes more expensive, our planet becomes more polluted, our internet becomes more polluted. Our servers become overrun by bot traffic, our gaming machines become too expensive, etc. etc.
I just want you to stop making things worse. I just want you to stop training more AI. It sucks, I hate it, and I want it gone.
AI helps me learn math now, what are you talking about??
I don’t waste time on unfamiliar notation, it provides me with context, suggests things I wouldn’t have thought of. And connects it to fields I wouldn’t have thought of.
We have personal tutors with PhD level knowledge for basically free if you know the questions to ask.
AI has already made mathematics better in the sense that it has greatly advanced what we know to be true (theorems).
The only way that it hasn't made mathematics better is in the sense of human mathematicians' career prospects -- and in this respect, it is identical to other forms of automation that the world, and especially computer programmers like us, have participated in in the past without complaint.
It's "worse for humans" in exactly the same way that first the Industrial Revolution and later computer programming made things "worse for humans", but the post you're referring to only notices that it's "worse" when they are the victim.
I agree with this actually. All of these things were good for some and bad for some, and these groups overlapped. All were good for (most) humans-as-consumers, and bad for (some) humans-as-producers, and the IR was also bad for horses.
I fear the same thing will happen as what I see in software developement. The volume of proofs that can be generated by anyone will be so big that it will overwhelm the system. Currently I really don't have the time anymore to check if all the bright results in computing projects make any sense.
And not only in software developement. In general, I see preprint servers getting overwhelmed by article submissions, AI generated articles. I don't recall a wave of CAD generation in the past.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to (and many more to boot.)
I would be thrilled! My only worry would be how to sustain myself financially if my expertise is no longer needed - worries like this I can definitely understand. But the simple fact that the problems I care about are getting solved? Awesome, more of that please!
Wonder if this is how G.H. Hardy felt reading Ramanujan's "proofs". I figure the real work begins now, the fact that a machine "showed the way" may become irrelevant 10 years from now.
That sounds more like a religion than science. Why not be happy that there is a new technology that helps solve (presumably) important problems that can have positive effects?
You'd be ecstatic until you realise "oh damn, how will I get enough money to eat?"
Sure, there are probably some mathematicians that are sad that robots can do all the proofs and such for them, but it seems to me that most of them probably would be happy with the robots helping to solve problems if not for the little issues that mathematics is their profession and in the current state of things, they need to eat and have a place to live.
And that is the actual problem. Let's just remember, the Luddites were not anti-technology, they were against the technology being owned by a small elite that could use it to take away their livelihoods. They were against the capitalists essentially throwing them into the ditch to starve, and we're seeing echoes of that in the current AI discussion and the reactions of mathematicians, programmers, artists, etc. Back in the 1800s it was physical and artisan manufacturing labour in danger, and now it's mental labour.
Maybe I am, but I'd argue that in that case I'm depicting literally all professions as rent-seeking, as people really want to protect their income and livelihoods from infringement that would endanger them. And at that point it's probably not useful to talk about it as rent-seeking.
If AI can do literally any job more efficiently than a human, then there's no need for human labour anymore and at least to me that seems that unless we get a radical transformation of our political economy, that will not be allowed to happen. You can't just put literally everyone out of a job, capitalism just wouldn't be able to cope with it and it'd implode, most probably because of the inevitable backlash that would occur for to no one being able to afford the basic necessities of life. It would be orders of magnitude bigger than either the French or Russian revolutions.
I'm no mathematician, but if being concerned about being able to keep my employment to be able to feed myself makes me a rent-seeker, then I will wear that on my sleeve proudly, crossing my heart, hoping to die. The misery of the alternative is too great to fathom.
Yes, imagine when cancer becomes a solved problem, and oncologists react online by lamenting the end of their life's work. They'd be viciously scorned and ridiculed.
> AI has destroyed a major source of "life's meaning" for many people who pursued mathematics.
I studied mathematics and don't agree with this at all, for several reasons. For one the entire point of maths is that it describes a formal system in which one can 'shut up and calculate'. Mechanizing maths goes back to Leibniz and Hilbert. Nobody should surprised that the big formalism with explicit rules you invented is the first thing to yield to automation, that's why it exists.
Secondly research, including maths for a long time has been a collaboration of people, institutions, machines and processes, even maths does not consist of Faustian heroes in caves having revelations.
And thirdly just because a machine produces a 500 page proof doesn't mean your job is done. Science produces knowledge. Knowledge is information made legible to understanding by people. So there will be endless work for humans to go over machine proofs and turn it into something we understand. Just like chess computers ultimately expanded human chess.
> So there will be endless work for humans to go over machine proofs and turn it into something we understand
I'm not convinced humans will be better at this than LLMs. Frontier models are quite good at handling even deliberately lazy/ambiguous eli5 prompts on complex topics IME.
>I'm not convinced humans will be better at this than LLMs.
they don't need to be. Any scientist is already surrounded by tools that are better than they are at anything. A scientist from 200 years ago would have the same existential shock if they see how a modern scientists works.
But that's to misunderstand what science is for, which is to expand human knowledge. And a tool by definition can only ever change how you do this, not that you do it because you understanding it is the point. When people say learning to program is now useless, what they really mean is it might not make them any money, or using the AI is faster as an instrument. But if you care about programming itself, about you understanding programming, nothing has changed, it never can. And the smartest AI in the world can always assist you, but only that.
> But that's to misunderstand what science is for, which is to expand human knowledge
I agree ideologically and aspirationally but I don't believe it's the economic reality of how and why most science is actually funded (and I think you agree based on your comment about not making any money).
> But if you care about programming itself
I'm...not so sure I do any more? At least, not any more than I care about using Java over Python, or C++ over Java, or C over C++, or ASM over C, or machine code over ASM, or an abacus over machine code.
> nothing has changed, it never can
We now have programs that can write any program 100x faster and better than even the best humans and solve the hardest math problems known to humankind that have stumped the greatest minds the planet could produce for decades. That, to me, is a change with profound implications for understanding the nature of programming.
The egos of these mathematicians is not what is important here, and they should get over themselves. The goals and values should be about advancing mathematics and, by proxy, humanity. It’s not about them.
That said, change is difficult for most. Let’s give them grace and have patience as they work through the stages of grief. Once they come to accept this new reality, let’s hope they can learn to embrace this new technology to continue the work of advancing the frontier.
I find myself sometimes wondering if the folks on Star Trek would consider themselves laboratory assistants to an AI, seeing as how the ship computer kind of works like an LLM: interprets voice queries into actions and takes actions, queries the database for answers, can extrapolate when asked to depending on how the writers are feeling... That kind of thing.
"My friends in cancer research are terrified they'll wake up one morning to find out that an AI cured cancer."
But more seriously, this was an inevitability for math, no? The brain has an upper limit on how many concepts it can recall, recombine, and synthesize. We're all finding out now what happens when every single concept in math can be perfectly held in memory.
AI solve my problem where I have to hand code all the time. I'm happier than ever. Math's analogy is they now get to find problems instead of solving them, then get LLM's to solve them or solve them together. I've been saying this, numbers go up, and LLM makes the amount of problems to solve go up, not less.
" As a scientist, I don't want to end up as a laboratory assistant to an AI."
The idea is, that the AI is your assistant.
Apart from that, I would also say get over yourself. We all have to. Arcane computer knowledge I was proud of having, that made me feel special can now be replicated by anyone with access to a LLM.
I still know how to build things and that is what I am doing. Just faster than ever before.
If you find your source of meaning in slowing down understanding and knowledge, you were never it in for the mathematics and some questionable motives. Find the solution within.
It feels like it's meant as career advice though. I have no idea what advice I would give to a teenager right now, but as a math PhD - math would not be on the shortlist, sadly.
I am an ex-mathematician who went into industry, I would say apart from CompSci/ML and physics, it was one of the most sought-after PhDs you could have (across tech and finance) - when I was entering the job market 10 years ago at least. No regrets.
Yeah, but how many of those mathematicians still do math?
It's like engineers in post-Communist European countries, sure there were tons of graduates, but 80% of them were doing something else than the thing they graduated in.
I actually remember that in an old interview (that I can't find sorry) Grant Sanderson said he moved in to YouTube because he thought it was a more promising career than being mathematician, it's interesting to see his opinion change.
Hmm, that seems like a pretty cynical point to make. He still deeply is in the field of mathematics, as a math educator. He even makes this exact point in this video, that communicating math is still a hard and respectable part of the profession.
As a math educator doing what you love you requires an audience.
Its kind of in Grant's incentives to push the interest for mathematics, because without an audience he won't be able to keep doing what he loves.
Like, my old uni has a history department, and had an Egyptian history teacher. This was at some point deemed a pointless use of resources because there was no role in society except for teacher of the same subject after that, and the classes shrunk, and she ended up getting offered a role in admin. She was not happy in that role.
I remember a post in... Reddit I think it was? where I commented on an early video discussion that he should teach online full time, because that kind of intuitive education was sorely needed. He actually answered the comment, along the lines of "that would be cool but I already have my hands full in $UNIVERSITY".
I think it was relatively soon after that interaction that he started doing youtube full time. I've always wanted to think I made a teeny tiny contribution to move the needle there :)
Yeah. All due respect to Grant Sanderson, he is both great scientist and great entrepreneur, but getting an entry-career advice from a multi-millionaire is probably not quite the best idea out of all ideas in a popular discourse. Especially if the field in question was famous for producing posts discouraging people from going all-in in it, for many many years even before AI craze.
There are quite a few problems with this video, IMO:
- Grant is a highly respected and popular YouTuber. He has a strong network, personal connections, access, and his income comes from an audience, not from output he’s measured on. He's perfectly positioned in this AI revolution to end up near the top of whatever human pile gets constructed, so he will not have the kinds of fears and anxieties that most people do.
- AI RSI is being actively developed and is likely to arrive within 1-2 years. I wouldn't consider this a fringe scenario; it's the main bet. Even if models stay weaker at theory building than humans, organizations will spin up 100k agents and the fire-hose of generated ideas will probably compound far faster than anyone can keep up.
- His remaining arguments are basically training people to problem-solve, and joy. For the next few years, I can see his particular niche doing quite well as infotainment, and he will probably make a lot of money. However, I don't really see people being able to join and partake in his industry 10-20 years from now. Also, if we project a realistic and grounded understanding of our current world onto the next couple of decades, what would give anyone the idea that political and economic systems would have any incentive to train people to problem-solve if AI becomes the real work-horse? Teaching will likely be defunded and turned into a consumption good (which it arguably already is becoming with these YouTube channels.)
- So, for me his entire argument boils down to... joy?
Others have already commented that this feels like unprincipled optimism, and I agree. I also think that because this is something made to generate revenue through a social media platform, it's inherently performative and on-brand. His incentives pull toward keeping his audience happy.
Unfortunately, outcomes follow incentives, not optimism. If our economy comes to rely on RSI-enabled AI, most people will simply have no place in any industry it touches.
>If our economy comes to rely on RSI-enabled AI, most people will simply have no place in any industry it touches.
Then there will be no economy. If anything, if we reach this level of economic automation, more people will have to find ways to occupy themselves and sparking joy through math might be the best way to go about it for some.
An economy can keep running even if most people are cut out of it. Production would just reorient to who owns capital, the state, and other AI systems buying from each other.
But, if I get the insinuation, this would still require a huge social change to absorb once broad consumer demand falls off.
As for pursuing math for fun: that would turn most disciplines into something akin to speedrunning, chess, or mountaineering. People would add constraints to make it harder for themselves and compete against each other, and that does motivate some - but not all. A lot of people want to be "on the frontier." If discovery gets automated, the remaining frontier may be physical, actually going places no one has been, and that might pull those people toward space as it opens up.
It can easily reorient itself (and arguably, already has) to serving the demand of a small minority of asset owners rather than the majority of people. E.g. people building luxury yachts and working to maintain them, working in luxury restaurants, maintaining luxury gardens etc. instead of working in roles that improve the lives of the majority.
Because most people are working on things that improve the lives of the asset-owning minority and not of the majority, the standard of living of the majority is not improved, they have to work more for less.
How many high-paying jobs today actually do anything that benefits the 'common man'?
First, "cognitive labor" is a form of labor - it's different vs. creative work, even though both use your mind. If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work. Cognitive labor is a form of labor. Let's talk about physical labor and leverage to understand how removing labor translates to time. On your farm you buy a tractor to replace your backhoe. If it is a hobby farm you get in the tractor and you're done super fast. Or, you can take that tractor, buy a bigger farm, and spend the same amount of time you'd have spent backhoeing, but in a far more leveraged way. You can trade removed labor for time in a way that suits you.
Second; the joyful moments we get from finding generalizable abstractions and nice solutions are an adaptation. Humans can climb infinitely high conceptual hierarchies - we'll never stop climbing, using the previous ones as tools to find the next. As we do, we gain joy with each discovery because. We get so much done with brains that run on 20 watts - are we tuned to receive a neurochemical reward for finding cognitive efficiency? If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
Third; everyone else is doing it, it's a baseline skill. Knowing how to work without AI is like knowing how to ride a horse. Useful and fun! Bedsides - only 150ish years ago horses were the only viable transport. Cars were new; toys for the rich. But cars got so good so fast that we eventually reconfigured whole cities. Your homework is to consider why and how horses got disrupted.
New divisions are emerging in the lump of roles humans had at work. AI takes away roles from your job and lets us do more with less. That's identical to every mechanization before it. It's killing some roles that make up your work, even as it creates new ones.
There's so much to be excited about. Fear is a rational response to change. But so is hope :)
As a software engineer, I found that a codebase that is LLM-assisted or entirely produced by agents gets harder and harder to understand intuitively over time. By writing code manually, you build a very precise mental model of how it works. The time it took was the price for that. Now, the time cost has been largely removed but the payoff also disappeared: it's essentially impossible to maintain the same mental model with the speed and volume of AI contributions. Reviewing code is not a substitute for writing it, and new contributions to the codebase are essentially bound to LLM usage. So now we're in a position where the codebase and its capabilities grow fast, but are not backed by the full understanding of the engineers. AI tools have become our crutch.
Math is very similar, and requires an even higher degree of mental understanding to produce advancements. The effort spent trying to prove theorems and connect theories pays off in deep intuition; removing that struggle significantly impairs our understanding.
So no, you can't "be done with that, and go do other great work" without paying the understanding tax. And over time that's just not sustainable.
A simpler analogy would be gym training: the effort expenditure and the strength gains are inextricably linked. You can't go in there and start lifting weights with a forklift while expecting strength improvements.
In the case of software development, businesses have decided that speed gains are more important than maintainability, understanding, and independence. Will the same happen in math? The future in which mathematicians become LLM assistants (as opposed to LLM-assisted) and spend their days "turning the crank" just to review what comes out is quite bleak.
The analogy is tempting. But gym training isn't what work is. At work the goal is not learning - it's delivering value.
Doing weights is not the same as say, updating the gym with shiny new weights; or migrating all the weights in the gym to metric. At the gym, if the current weights need to go and new ones installed, a forklift will one-shot it.
Seeing the difference empowers you to choose the right approach for the right situation.
> If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work.
If your painting can be painted in partnership with an LLM, wow!
If your essay can be written in partnership with an LLM, wow!
If your painting portfolio website can be written in partnership with an LLM, wow!
If your museum show can be designed in partnership with an LLM, wow!
If the placards next to each of your paintings can be written in partnership with an LLM, wow!
If the car that takes me to the gallery can be designed and driven in partnership with an LLM, wow!
If the newspaper or novel that you read on the way to the gallery can be written in partnership with an LLM, wow!
If an LLM can give tours at the gallery and answer questions asked by visitors, wow!
If an LLM can write the music that I listen to on my way out of the gallery, wow!
If an LLM can synthetically perform the music, too, wow!
> If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
I don't understand how a person can say this with a straight face. There has been so much discussion of this, and so many reasons have been given, that one can only assume that, if you're asking the question and you have thought about the issue and read what people have said, you're not only asking rhetorically but have some personal reason for insisting on a frankly pretty frustrating, borderline insensitive insistence on being positive. I'm not trying to be snotty or rude. I just want to say that to me there is something uncanny about your comment, in its total blindness to any of the reasons someone might not only disagree with you but grieve the death of, say, their academic discipline in its current form -- and in its weirdly breezy lack of empathy.
Are you suggesting that if an AI could do all of those things to your satisfaction you would not be extremely impressed.
I do have empathy for people who see the world changing and are forced to adjust. That can be uncomfortable, but it is something that is inevitable with the changing world. It has always been this way, There is very little need to make swords these days, and as anything becomes superseded there are people that are attached to the old things and there are people dependent on the old things.
I think it entirely possible to have sympathy for their position while disagreeing that the solution is to prevent change.
I don't see this as a breezy lack of empathy. I see this as a hand reaching out and saying 'Hey, you can come this way and things aren't so bad after all'
My daughter is 21 months old. I love her more than anything and want her to develop into the best version of herself. Let's say I can press a button and give her perfect command of English. Another button gives her expert-level command of advanced mathematics. Perfect hand-eye coordination. Emotional self-regulation. Empathy. Etc. Keep listing every desirable trait and skill you can think of. Hit a button. Suddenly she has it.
I would not press it.
Yes, if LLMs can do all everything I listed, I'll be impressed. I'll also want nothing to do with any of it.
As I wrote in another comment, I want mathematicians -- in their current form, doing work as they traditionally have -- just as I want writers, philosophers, etc, because this is a better world that makes people better.
OpenAI's proofs do not make people better. They do not make our lives or work meaningful. Quite the contrary. OpenAI has clear-cut and salted fields that people have been painstakingly, lovingly sowing and cultivating for generations -- profoundly ugly actions that do real harm to some of the best of what people are and have produced.
If I were a person willing to hit that button and 'upgrade' my daughter, I don't know whether I'd be able to live with myself. I'd feel as though I'd killed her or at least done profound, unforgivable violence to her. She deserves the chance to grow into the best version of herself. What companies like OpenAI are doing is, if their plans pan out, at least as horrifying. It isn't progress. It isn't good for people.
We're not taking about attachment to old ways. We're talking about attachment to human value.
Thank you for putting this so eloquently into words. I feel the exact same way.
The journey is the destination. I don't care how many checkpoints you can breeze through, if you don't grow, have an experience that transforms you through the process of doing it. And if you're just ticking boxes by means of having a machine do it all for you, there was no need initiating the process in the first place.
I am not talking about producing tools that are means to an end here. I am glad we can make millions of socks a week by means of automation. But intellectual endeavors are different.
The point of doing math is not proving theorems. It's to discover the intuition, the underlying phenomena, internalizing them and adding to the human understanding of the problem. Writing out the proof is just the incidental outcome of that process.
If no human learns anything, if we just start producing testaments to a human null process where no person has emerged strengthened from it, we are no better off than we ever were. We are just producing empty and meaningless representations of something which is not there.
If your daughter had cancer and you could press a button to make it go away, would you press it?
If so, what aspect of that makes it different? It is a change in the same beneficial direction. It is an intervention against what has happened naturally.
Similarly if she lacked any empathy and you could press a button to provide it? This would be the same direction of the same property, just an intervention from a different naturally occuring starting point.
I make no claim of the merits of OpenAI's immediate behaviour. I am commenting on a world in which things like this can be done, and like Grant Sanderson, I see a world of opportunity for understanding and learning for the joy of appreciating the problem and the solution. The only thing that seems to have been lost is that a human may no longer gain the prestige of being the first to discovers something. That should pale into insignificance to the benefits of understanding a thing. I'm not even sure if you should consider prestige as a healthy motivation to discover things.
Right now AI can provide a proof that is either valuable or not. If it is just the last page of a novel without any of the chapters then it hasn't given us mutch at all. The problem isn't in what it has provided, it tha't we've been using the wrong measure of merit.
If it does provide a full result with a rich explanation that people can understand then it has undoubtedly provided something that benefits the world. No human is awarded prestige for the discovery but that has always been an unfair measure.
If you work all your life on a math problem only to have an AI produce the result before you, how is this meaningfully different for your experience to working all your life on a math problem only to have another person produce the result before you.
If there is something that is unknown and could be proved true by path A and proved false by path B by definition nobody knows which path to follow. What happens if two mathematicians attempt this problem one going down each path. If an AI produces the result before they finish have they lost to the same degree? Only one of them had any chance of gaining the prestige. Did the other lose nothing? Was their life wasted? I don't think so either way and the only way to consider that work not wasted is to consider the effort to understand to be the thing that is valuable, not the result at the end.
If a solution is found by a human when there are people tying multiple paths, the one who guessed the correct path gains the prestige. That doesn't seem like a fair way to reward effort.
If we want understanding then AI can help.
Chess has had this moment. Computers can play chess better than people. It has also been a great benefit to the understanding of chess precisely because they value the how to get there over the result.
Prior to modern chess engines you could hypothesize about what the best move might be but you could never know if you were right. The fact that chess engines beat people so consistently is because often the guess is not right.
Chess engines gave us the ability to look at a game and see if if a player could have made a better move. They could then look to see why it was a better move. People then learned how to play better. They still play against other humans because they are testing each others understanding of the game, for that the computer is set aside.
Computers playing chess better than humans improved chess for humans.
Is there a compelling reason why that cannot be true for other things that they are better than.
Thank you. By far the best comment in this thread. As a dad this really resonates with me too, and even though my kids are a little bit older than yours the feeling is very much the same. We're automating away those things that make life worth living now.
I think it would be much more of a change now, if we ban LLMs entirely and force everyone to do everything without any form of chatbot to help them. I would sympathize with the people who can’t handle this change, but it’s gonna happen, I think they should get with the times and adapt to it. I think it is wrong of you to try and prevent this change.
Actually I think we need to go further, we need to make an example out of the people who spent a trillion dollars building a product that is universally hated to try and make a buck. They need to be completely ruined financially, now that would be a real challenge, I sympathize with those adversely affected but it needs to happen if society must progress to a better place where humans flourish more.
AI needs to be instructed to do a thing. To use the "steam engine designing another steam engine" analogy, why do the big labs give the highest pay of all to their prized researchers? Why do they take steps to prevent poaching? Surely a non-expert could prompt a model "find a superparameter combo that makes an amazing model" and the next gen model would emerge! The AI should be able to design a better AI on its own!
Why do the labs have thousands of employees? Lets think about this...
Who's designing the evals needed to validate the model quality, who's deciding what goes in the system prompt? Who's negotiating to buy training data from hundreds or even thousands of data vendors? Who's responding when the Internet goes apeshit over some prompt tweak that makes models over-verbose? Who's out there listening to users and feeding what they say back into the product pipeline?
Computers????
However automated things get, that quickly becomes the new baseline. Customer expectations are always going up.
And as soon as humans figure out how to automate any of the things listed above - it becomes part of the new baseline too. It's always advancing. To beat the baseline and be competitive, you need humans. No matter what. No matter how automatic the automated things get. Always and forever. Because you need someone to drive, to find the next automatable thing and automate it - and to prioritize where to search for automatable things.
> Always and forever. Because you need someone to drive, to find the next automatable thing and automate it - and to prioritize where to search for automatable things.
If we look at history of automation throughout the times it always decreased the amount of people needed to do the job. If you can't see a future where this new steam engine learns how to do a better steam engine, then you are blind. With the trajectory we're on it will happen sooner or later, and most people are having existential crises because the amount of humans required to be "in the loop" are decreasing increasingly fast.
I agree the people needed goes down - but will add a nuance.
Roles go away and fewer people are needed to do a thing, but I think it's good! For example the number of people on farms decreased orders of magnitude over the past say, century - yet we still feed everyone. Farming got mostly automated and got insanely more productive per human.
What happened was those people who would've been needed on farms went and did other stuff and the economy got way more complex but also that new complexity let a lot of more awesome things got provided for a lot more people by a lot more companies, a trend that continues today.
If you want to be a farmer good luck; it's harder to get started than it was say, 50 years ago - so why bother when there is no net new demand for farmers and there are also many better ways to make a living.
That's what'll happen for cognitively drudgerous work vs. creative new work.
> AI takes away work and lets us do more with less - just like every mechanization that came before!
No, it's not the same as mechanization. The fundamental difference, and why I find it illogical to argue either for "AI will open up tons of new work avenues" or "AI will kill all jobs" is that it all hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
If the former is true, then yes, there will be a lot for humans to do. If the latter is true, then no, there will be no reasonable cognitive role for humans to play (beyond perhaps for some legal, "nostalgic" reasons or what not). So whether one decides to be optimistic or pessimistic really depends on if you think AI will stay at a level below humans. I really don't know, so I'm not "taking sides" in this debate.
It's certainly possible that "the special sauce" that provides human consciousness and sentience (that I believe is not there for LLM-based AIs) provides some key ingredient to some forms of intelligence (particularly when it comes to originally) which LLMs would not be able to duplicate.
For example, much has been recently discussed about how OpenAI's math results, as impressive as they are, remained within "the convex hull" of existing math literature. Thus, some have argued that the way LLMs work will keep them squarely within this convex hull, and also there seem to be clear examples from human history where humans came up with breakthroughs that were outside the convex hull of ideas that existed at that time.
There has been a lot of recent debate, both for and against, this idea that current AI approaches are limited to this convex hull. So I'm not going to try to convince you one way or the other, but I do think it is at least a plausible explanation of how/why current approaches end up hitting a wall.
I'll also show my bias which is to say I certainly hope they hit a wall, because I don't understand how anyone can think that humans won't be truly and completely fucked if AI ends up far surpassing human intelligence.
the convex hull argument has recently been under scrutiny as well.
some proofs of famous conjectures (for example unique games conjecture) have been described as creating new, insane, almost alien ideas. Scott aaronson has a blog post on this.
> ...hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
I agree with you, just wondering your thought on how we will know the latter has come true? As I understand it, you're describing ASI, not AGI. The way I personally define AGI, we are already there.
On one hand it is hard to fathom not being the most intelligent thing around.
On the other hand, if we are going to survive as a species for a long time it probably depends on us learning how to not be the most intelligent thing around.
Even if it leads to our demise, I don’t think willfully holding ourselves back is the way forward
Yeah, honestly I am worried about "the psychopaths who walk among us" who basically argue "Yeah, we may end up building SkyNet, but tough shit, can't stop progress!"
I think one form of cognitive labor will remain: What do we actually want to do/build. And this is simply because AI does not know our internal world. Maybe in a few years with some kind of BCI that is extremely good. But I don't see it happening at least for a few years.
> Yes but what about all the horses replaced by machines?
The point is that people, like horses, can do other things. Humans don't even have to be better than robots at anything. It's the principle of comparative advantage.
> A good precedent is mechanized agriculture. When machines effectively replaced most humans in agriculture, unemployment did not rise to 90%.
I don't consider this a good precedent to the AI situation at all.
When this happened, humans went off and started doing what we now consider "knowledge work" (well, after a brief stint in factory work, where they also got displaced by automation). They escaped massive unemployment by being smarter than the tractors and mechanical looms. But how do they escape AI job loss when AI becomes smarter than the average human? or smarter than the smartest human?
In prior displacements humans moved up the stack. There is no longer room for them at higher levels of the stack if AI beats them at cognitive labor.
And this is why we must ensure that the AIs get aligned towards humanity and crucially that they don't get aligned towards capital, which seems to be the current trajectory.
There's a better chance that a humanity-aligned AI would make sure that humans have something to do and keep us alive versus a capital-aligned one. At the same time, if AI would be the deathblow to capitalism, that'd be very, _very_ ironic.
No matter whether AI caps out or when, humans will be driving.
That said, other humans can and will put AI to use in ways that don't benefit humanity. It's actually already happening - newsfeeds waste hours of people's lives and attention; give teens low self esteem etc etc. and guess what. Society is adjusting - governments via legislation, device makers via screen time limits, communities by spreading the word and raising awareness
Smart AI wielded by people without your best interests in mind may be tough to counter; but you don't have to do it alone: humanity is getting wise to the threat. We don't have great tools but it'd be against the grain of history to assume we won't come up with them in time. Can't give specifics - as they say, predictions are hard, especially about the future..
We've made it through bigger more violent upheavals and we'll make it through this.
This is the same naivete that I saw in coding some time ago before most people finally accepted there is no going back and the times of writing code by hand are gone.
And the guy is not a mathematician primarily - he's a Youtube creator and entrepreneur. I liked a lot of his videos but now I usually just ask the LLM for detailed explanation and I can probe it as much as I want if something is not clear enough.
Education will also take a huge hit, you can't really beat an almost free supergenius that has all the time in the world to explain something to you in as much detail as you wish.
It is not, and for the same reason it's not over for mathematics. For anyone doing anything truly novel, and yes there are still software engineers out there doing that, it's still inept.
It's de jour to leverage formal verification as LLMs are quite good at looping it, but that's still a tool we had to invent to solve problems. It'll be truly over when we're being outpaced in the realm of invention but I have seen absolutely nothing to suggest that has meaningfully occurred at all. Coding by hand is not gone, there's just less of a reason to do so now.
I’m a cheerleader for the Khanmigo AI tutor effort. But, apparently so far they are discovering that the hard part is getting the kids motivated to actually ask the AI any questions.
3Blue1Brown does an amazing job of making math interesting to learn in itself. As opposed to the hundreds of millions of kids told “You just have to learn it or you’ll be dumb. Keep up or you’ll fall behind forever. Go!”
The vid calls out explicitly that math education is a primarily a motivation problem and I agree. One way or another, we need a lot more focus on that.
Lack of motivation can be a problem and I love 3b1b videos. However, if you want to truly learn, you still have to sit 30-60 hours on a subject to be able to solve problems. No motivation will replace that.
When you have limited time to learn as a student, you either have the smarts to learn in the limited time or you cheat.
I can beat this “supergenius” - I hire a professor that knows exactly how to teach and what to teach. This professor isn’t rolling the dice every time I ask them a question. Boom.
Your paradigms are showing! I'd argue that if your POV is strictly "That's not how it's done," then it's time to re-read Kuhn's Structure of Scientific Revolutions.
There has never been a better time to pretend you understand anything aided by LLMs deluding yourself into being an expert, yeah, that's how the video should be named :/
I can't help but feel how this is all industry-planted, and I wouldn't argue its too far fetched.
I could be fully wrong here as I am not from the field. But how is this different from let's say a ramanujan-like genius dumping a bunch of solved problems with not yet understandable ways of getting there?
It seemed riveting enough for some mayor mathematicians to "decode" his solutions into readable proofs?
The only difference I spot now is that it was not an Indian man, but a machine. If that bothers you still, it seems less about the art of the craft being taken as it seems to be about who has taken it?
The difference is partly that in your hypothetical the man who solves the problems doesn't become a commodifiable tool. It doesn't become possible to increase your spending on him to solve a problem. It would be recognized that he is in a category by himself (and hopefully a better writer than the models) and therefore would not change how others do their work. The list of differences could go on and on.
AI will be much more powerful than ramanujan. ramanujan is just one person with limited energy, but many instances of AI agent can work in parallel and attack all open problems at once
Reflecting on that a year later is interesting. Agents have become REALLY good since then, and I consider the "writing code" side of my profession to be largely annihilated. Some days that's really hard to accept.
But I think Grant's conclusion about math still largely echoes what I wrote about software: don't underestimate the social aspect of these activities, and if anything AI has made the social side more important. I deliberately avoided declaring, "now is the best time to learn to write code". I suspected that skill might be going out the window. But learning systems thinking and the social skills needed to connect people's dreams to reality continues to be an important art, an art I still have the privilege to practice every day.
And if we do reach the "anything you can do I can do better" stage, then, as Grant said, that's a hard to imagine world, and one where "it can write really good code" might be the least of our problems.
At this point I'm ready to call it... LLMs aren't going to ruin my job. They're amazing, they're useful... and the problem remains that to a first approximation human beings are uninterested in spending all day talking to a computer, whether through a classic IDE or through an LLM. Specifying a problem enough for an LLM to solve it, even if we stipulate one that does it perfectly, is already more than most people want to do.
You also aren't going to get an accountant running 4 simultaneous streams of AI-driven development and working through an AWS issue when something goes wrong.
The problem is you're focused on 1st order effects. I presume you work at some company that sells a product or provides a service - what happens if the demand for that evaporates because the clients can do it themselves or the market has been flooded by much cheaper alternatives created using AI? Or people who bought the product can't do it as they lost their jobs to automation?
Second, if "all software vendors in all spaces get wiped out" was going to happen I think we'd be seeing more of it already. Yes, there is support for some software vendors possibly getting wiped out... but, then again, you can't look at a bad vibe coded implementation of "the entire Adobe suite" that was rather overblown in the press coverage and forget that Adobe also has AIs. Instead what I'm seeing at my own workplace as we ponder the question of "should we replace this service we buy with some local vibe coding" is still remaining but we don't want to support that. Can we replace Confluence with vibe coding? Yes, but that was true five years ago too and we didn't want to do it then, either. We still don't want to do it. HN commenters have always overestimated the desire everyone in the world has to become programmers and take responsibility for everything.
One wonders what percentage of those who are certain that vibe coding is going to nuke all software vendors can't even be arsed to self-host a Jellyfin or VaultWarden install... which is way easier than vibe coding the whole of those things from scratch, and we're talking about people who are already programmers. Physician, heal thyself.
I hope you are right, but I think there will be a lot of reshuffling nevertheless if only because the shape of the work has changed so much. A lot of people who hated developing software will suddenly find a passion for it, a lot of people who were good will find they can't stand this new world.
I agree. I think the days of the developer who hated talking to anyone but is still very valuable are over.
I think social skills are much more important today because one person can do so much more but this person needs to talk to many others to know what to build.
And this is why I am likely to leave software. I actually really like people, but I am autistic and not especially good at talking to them, and it's quite drianing to do so.
I will miss coding, but I had a good run. Time to learn a trade. I don't begrudge this fate.
Why would you leave software? Sitting down and working in silence and thinking is still a very rare and valuable skill, the talking part is not so much.
If AI solves all coding and software then we are not going to sit around talking, it will be the time to sit down and do some very complex deep work that needs silence, concentration and understanding.
For you it will be paradise, you can also just point all the people to talk with your agent instead of you.
I'm trying to think of an exception but I find it hard to disagree. Even if you know exactly what to build, it's pretty hard to get any adoption without being aggressively social. Find a good extroverted friend, maybe?
No… the person who's going to do well is the one who doesn't have to ask what to build. The one who has to ask is no better than an AI, except they start out wanting to ask, rather than starting out with no interest whatsoever until they're prompted to have one.
When everything you ask for is instant and valueless, even asking becomes meaningless, and everyone is waiting to see something they'd not thought of.
Then, a thousand thousand copies, immediately… but also, watching that person like a hawk to see if they can do it again. That's the future. A lot of people will just plain become unable to think or intend anything on their own, or even want anything.
Somebody still needs to determine what the company system actually look like, that someone is still probably a programmer, it doesn't matter anymore if that programmer is also a good coder.
by the way it feels to me that teaching is one of the most satisfying jobs on earth, you could (and should) be passionate for hours long in front of your students, that's amazing. as a programmer it seems you'd only feel passionate for like 5% of your work, even before AI it wasn't all that joyful, you had to attend boring meetings, debug legacy code bases, trying to make sense of the bad decisions other made (including yourself), it's fine, it brings food to the table.
I think the myth of "passion" has affected way too many youngesters though. You can find meaning in many things in life, and there are already way too many people who kept chasing their "passion" yet at the end realized it didn't bring them real happiness.
Maybe this AI thing is good for us after all, maybe we should take a pause and answer the harder question.
Edit: and yeah, even teachers probably have lots of chores and boring parts of the job.
That is why schools should have physical punishments. "What is the purpose of learning this? What a stupid question? To not get additional lashes, obviously"
I like the optimism but it might be a case that actually there is nothing left for humans to figure out in math 2.0. I wanna be wrong and mathematicians will figure how to regain the control. Software developers lost it and turned into meat proxies.
In the essay Hackers and Painters it was mentioned that there is a project approach to learning and an academic one. The idea of pet projects is killed by language models, because what you did on weekends, a language model now does in half an hour. So you can try the other approach: maybe you should have more general knowledge right away, best practices, so more of an academic approach. In the academic approach you learn from the best reference examples, develop taste, and only then recognize what is good or bad and build your own. But here too you can see that LLMs iterate much faster, while you have to collect patterns for years, and you will also always be in the role of the one who is behind.
> The idea of pet projects is killed by language models
Only if the goal of a pet project was the end result. In my experience pet project is all about learning new things and exploring the unknowns. LLM finishing it in half and hour does not achieve any of that. Although it can be a good assistant.
Before, I would write an emulator of an old console. On weekends I would debug why the game shows garbage instead of a picture, compare opcodes with the documentation and learn from my own mistakes. And the emulator itself would be valuable as an artifact, because it holds the experience I accumulated.
Now the same thing can be done much faster. Learning from mistakes disappears, only high-level templates remain which looks similar to the academic approach.
On the other hand, you can set up an LLM so that everything goes gradually and you learn like you used to. But that's more like what I would call pet archaeology or something... Learning the tools doesn't give as much benefit anymore, it's more like a reconstruction of past events.
I have setup a sistem where I leverage LLMs and agents to replicate scientific papers, cs and related fields, especially ML ones, and that's what I do in the weekends now.
I think a lot of "mathematicians" are saddened by the sudden realization they are not even interested in it and were only in it for status and prestige. A lot of them are such pretentious tools that they willingly wasted their lives doing the absurd PhD rituals. Academia is dead.
What about the people who are in it to think deeply about mathematics questions? It's a lot harder to feel like that's worth doing when there's a black box with a crank that takes money in and spits out mathematics answers.
Like calling Lee Sedol a pretentious tool for retiring in the face of AlphaGo. If you really do mathematics for the enjoyment of doing mathematics, following a roughly unbroken line of tradition for at least a couple hundred years, an alien computer mind showing up and smashing everything would perhaps be upsetting, don't you think?
People still play Go. And they still play chess. In fact it's more popular than ever. For activities people truly enjoy, the alien computer mind showing up and smashing everything doesn't change a thing.
Nothing is stopping anyone from thinking deeply about math. The angst here is about whether they can get paid for it or not.
Mostly Funding. Then each other. Then the myriad trivial yet bureaucratic things of daily life. Then research. I'd put research at like 10% of a week, so maybe 5 hours total.
I have been feeling this way about software. Don't get me wrong, there are some things I am very interested in and would work on for recreation (macros!), but a lot of it I'm less interested in.
Frankly, despite the obvious financial worries, it's been a little freeing. I can go do something else (because, uh, I may have to).
3blue1brown has the absolute most educational and entertaining videos. Always fascinated by his animations which are custom programmed by him. I also appreciate the diversity of topics covered from deep math to software to science.
There's never been a better time to be a professional mathematician, perhaps. Just like there's never been a better time to be a senior software engineer.
An 18 year old entering university today will retire somewhere in the 2070s. Is mathematics, or software engineering, a promising career path for the next 50 years? No, it's most certainly not, and anyone suggesting otherwise is delusional. I don't know what would be a good career path, but most certainly avoid anything that AI is having the most success at in 2026.
I'm on the wrong site for this, but isn't it interesting how we don't ask what is the most interesting field I can join, but rather ... how do I stay employed with this for the next 44 years? Seems to me we missed the entire point and just accept it as reality and that it has to be this way. I'm not asking this to be snarky or smart, I'm just genuinely curious why everything seemed easier back in the day.
Not every field has an equal number of vacancies. There are a few people who study Art History and get a job as an art gallery curator, etc. There are many more who end up as baristas.
It's fine to follow your dream, but just make sure that your dream wants you too.
It also helps to have rich parents, if you grow up poor you understand the consequences of choosing the wrong career path can be devastating. Some people have the freedom to experiment and still get a soft landing, other people need to get it right the first time.
If AI came about 40 years ago, it would have been much more restricted and advanced much much slower.
But politics does not care for the average worker anymore. Every democratic country is slowly turning geriatric, so due to how democracy works, the will of the OLD is what runs societies. And job security is not one of those things, when the biggest voting block does not even work.
Yeah, there isn't anything wrong with encouraging people to get into mathematics
But recommending it as a career, might be delusional, maybe harmful? (Although people say that about artists too)
Ai will yield a higher demand for mathematicians, we need more people to understand the math being solved. We also need more people inventing math problems.
People who want to solve problems themselves should go on to invent them without posting them on the internet until they're solved.
personally as a math phd student, LLM centric math feels soulless and ultimately is not what I entered the field to do which is to personally make mathematical discoveries with my own brain and cognition, and not direct a discovery machine.
Yes, cue the: cope seethe, selfish mathematicians, care only about personal glory, more theorems = cancer proven, more knowledge>less knowledge, e/acc etc. etc.
I've heard all these tired arguments many times. Whatever - I concede - you're right and I'm morally wrong and bad. Just don't expect people to study this subject which is basically being turned into biology (spend hours sitting in a lab babysitting equipment all day while watching a movie - it's what most bio phd students i'm around seem to do, no offense meant to bio phd students, i'm certain their studies are orders of magnitude more impactful to the society than mine).
I think you guys will go through the same kind of divide that SWE went through.
There is a number of SWE and adjacent IT professionals that do enjoy the LLM assisted work, I'm one of those.
There's a number of them that absolutely loathe it.
Your point about biology does not sound fair, an ex of mine worked in the field and that is not at all what she did.
I think a lot of these reactions by mathematicians are more akin to group theory than anything else. Reality is that things will naturally sort themselves out and there will be some role mathematicians play in all of it (most likely). To me it seems the timeline that some skill essentially gets retired such that if you want to keep doing it is more like "historical re-enactment" is getting quite short. Things like manually coding something is going to be a hobby. Some aspects of math are going to be a hobby, and professional math will be all about pushing up against the edge of what we can do mathematically with AI.
As an applied mathematician who went into industry and has friends still in academia it's quite interesting.
My view is that the people who think doing maths is about being able to knit maths quickly and correctly are quite sad.
But for the people like me who bound themselves to computers a long time ago, it feels like a revolution. Sure you might now be simply tending your garden of machines and allocating capital and resources like a Gardiner picks seeds for various sunny spots but you can now do a lot of stuff and for people were good at gardening but not knitting it is a game changer.
Too early to tell, but IMO unlikely. Let's see what his take will be once an AI can propose a topic, write the script, animate, and narrate a good educational math video.
He won't care because he has established position and is set. It will be just like everybody else - if the individual is at the top of the food chain then he/she is all over it how you are using it wrong and how you should use it (don't forget to follow and subscribe).
Yep, that's what I see in the CS field -- people at the top are advocating AI and don't understand why the hell the others are hesitant. I meant the top engineers, not the management. I look up to them because of their skills, but that doesn't mean I need to agree with everything they said.
But you already have Claude-directed videos that utilize OP's manim project (which he uses himself to do 3b1b) that anyone else can create. Grant open-sourced manim and now anyone can point a model at it to create their own 3b1b-like videos. They're popping up all over the place as Opus 5.5 demo videos just in the last few weeks. So... AGI?
I guess I wasn’t clear, but using manim to make videos is not the hard part. The hard part is making them engaging and enlightening, and whatever else you want to attribute to 3b1b videos which make them a joy to watch and learn from.
I tried watching 3b1b over the years, really wanted to enjoy it. But I never found the way he presents things intuitive and never got a palpable intuition that helped me with math classes or work.
I saw some clearly AI slop made videos and got much better understanding of topics, since they don't do foreshadowing for an awe-inspiring connection that we'd admire together after 15 min videos, the clankers just get to the point. Not claiming those videos are too useful either, but I did however see accelerated learning gains from asking LLMs to explain (and do Bret Victor-style small interactive demos) math and algos, something I have never experienced from any of the educational STEM Youtube channels.
Even if you find them intuitive, they produce no learning gains for anyone. Take a lin alg test, watch the 'Essence of lin alg' videos, take comparable test again. I guarantee you won't see any change even if you 'understood matrices better'. They are pure mathporn.
No learning gains? I teach linear algebra. I can assure you that students who watch and study the "Essence of linear algebra" videos (which I recommend on the syllabus) do better on my tests that those who don't, because they learn stuff from them.
It's much more likely that the students who take the time to watch supplementary materials are the ones who'd do better regardless of the quality of the given material. If you have access to fresh learners, I'd say it's a good opportunity to test how good those series are.
I'm not sure anything I say can convince you, as your mind seems to be made up already, but my experience has been that those videos help my students understand the concepts of linear algebra, comparing the mastery level now vs. before the series was published on YouTube. Especially when it comes to getting a feeling for what a linear transformation is, and how the properties of matrices echo the properties of the transformation they represent.
As for "fresh learners", I can provide my own son, who watched the series before taking his first linear algebra class, and says that it helped him a lot.
This is not my experience. Having an intuitive grasp of e.g. the graphical interpretation of the determinant instantly lets you figure out most of the key determinant properties without having to memorize them. That's the primary thing you get from intuition imo, having a sense of what must be true without having to memorize or prove it.
I'm actually quite optimistic, was pointing out that, at least to to me, AI slop already produces better results than big educational content creators. For something concrete, even if not classic math, I credit direct LLM interaction highly for accelerating my understanding of CPU design and compiler tech.
fwiw the fact that brains work fundamentally differently was my big penny dropping realization after digging into what LLMs are doing. Everything (I assert) a brain does (the function between inputs and outputs) is due to training data. There is no "instinct" and there is no "ROM-driven way to think" in any brain. It's training data all the way down. As a consequence different brains do indeed think in fundamentally different ways.
This is so fundamentally divorced from what we know about cognition in humans or in animals. The idea that we are a pure tabula rasa and only shaped by our "training data" is absurd and false. Just look at the amount of data we need to be able to do things relative to ML models. Look at animals which can do complex tasks moments after birth. We're deeply, deeply shaped by instinct.
I suspect people who are deciding what to study will do so on the basis of a multifactor view of what interests them, how they predict their career will be after finishing said study etc.
There ought to be people watching his channel who wonder whether given all these AI advances math is even worth studying now.
Grant Sanderson tries to explain why getting into math remains worthwhile in an AI era. But his audience is composed of two groups -- people who won't follow his reasoning, and mathematicians.
Someone once described a mathematician as a machine to turn coffee into theorems. Okay, fair enough, but what sets mathematicians apart is that mathematics wasn't a choice.
It's possible that Sanderson doesn't get this, but people watching his video either will never understand his argument, or have always understood it.
In other news, there's never been a better time to be a software developer. Come to think of it, there's also never been a better time to invest in learning copy-editing and proof-reading as a side hustle. It's a Brave New World. Everything is fine, the demand just got expanded, the pie got bigger, nothing more. New doors will be opened, nothing has changed; in fact, everything improved. Stochastic parrots are no match for our carbon-based g.
I doubt demand expanded much. I mean there is just that many games/whatever apps that the whole humanity needs. Maybe ti will go up a bit, like 50%, but getting 10x (or very easily 1000x if we just vibe code them) in supply doesn't change that.
I mean if you read some history it’s not the first time complete workforces have been replaced. It doesn’t mean the same jobs stay, but usually there will be something to do.
Whilst I agree it’s not conclusive to assume that just bc something happened the way it did in the past it will happen again. I think there’s still 'reason to believe'.
My answer to your job is that more jobs move from secondary to tertiary sector (entertainment). That has happened usually.
Problem solving, critical thought, logic, creativity are always going to be valuable.
In a way ai is turning programming more into maths - you write a natural language description of the problem - a proof / program - and then translating that into machine code is a lot of work / abstraction. For example look how much it takes to turn relatively simple mathematical statements into lean. That I guess is going to be the future.
I would encourage everyone to learn the fundamentals still because you will need discretion and to be able to think at a more abstract level.
However its funny that its only NOW dehumanising/demoralising now when its white people losing jobs to the capitalist machine in the imperial core, and not the slave silicon miners making gpus for gamers.
> Are those capabilities valuable if machines are better at all of them than you?
Machines have been doing arithmetic (add/subtract/multiply/divide) better and faster than humans for 70+ years. I would ask anyone making this claim, "are you OK if your children do not learn basic arithmetic?"
Is there a transcript somewhere? Unless you're willing to pay me to throw away 40 minutes of my life listening to a stranger when it could have been an email
Yes, the video has a transcript available. You'll find a "show transcript" button in the description.
That said, you'd be missing a bunch of hand-made illustrations and animations from one of the best math communicators in the world. If that's not appealing to you, I'm not sure the transcript will do much for you either.
> The worst thing you can do, is to try to gaslight yourself into believing AI has apparently made your life great.
It is make like better. You're just invested in ripping out others' tools for your own satisfaction.
> Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well.
The difference between this & the backdrop of Dune is near 0, with its issues clearly outlined in the book: You want the system that existed in the 2010s to remain as-is & ossified for your personal enjoyment.
If it’s a question of whose enjoyment matters more yours or mines, let’s put it to a democratic vote? Let the public decide whether we should ban AI or not. If it turns out that America votes to allow Gen AI full swing then I’ll leave it be, somehow I strongly suspect they’ll do the exact opposite. At which point, you should adapt to what the public wants.
I haven’t watched the video, but likely it hasn’t answered a question: why math? Why not physics, neuroscience, philosophy or history? People claim math is both philosophical and art, but is that a sufficiently good reason to pursue math as opposed to other careers?
A lot of arguments seem to try to cling to the “old” way of doing math: staring at the blackboard for hours, wrestling with papers and papers of equations, and do forth. Well, chess players went through a similar transition period: carrying books of openings and such, to chess database, to chess engine and now AI. And at no point I hear chess players complaining that we have to study chess the old way.
No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch."
Mathematics is a fundamentally cooperative match vs reality. Many mathematicians, AFAICT, saw their key skill in manipulating a wide range of highly abstract notions. Now machines just got too good at this skill, and they can work 24/7. This may feel terrifying for some. Others would bet that machines coöperating with humans will be more successful than pure machines, so they feel empowered. What's beyond doubt is that the entire field is being shaken.
In boxing, chess and many other competitive sports, the actions of one player directly influence and have an effect on the other player. Golf is merely a parallel challenge, where both are playing against each other but not influencing each other directly (sure maybe there are some psychological effects that can occur between the players, but no strategical impact by the actions of one player on the other).
The players know if they're ahead or behind, which affects how much risk to take. Do you take the safe shot, or go for the tricky shot that could potentially save you a stroke if you get it right but could lose you more if you fail?
You'll see a golfer perform at least a few strokes different depending on their partner, and at a pro level that's the difference between "in the money earning an extravagant living" and "washed out on day one, thinking about taking a different job"
We can and should have it as something that people do in the future because we have the resources for everyone to do so.
In your personal experience and based on your knowledge of history, is this generally how humanity works?
And my comment was cynical: when has lots of prosperity lead directly to its fair distribution? Almost every redistribution process required lots of people dying, first.
They haven't had influence over their future since before they were born.
2. Quantum randomness is the very opposite of control over your behavior. Instead of doing what you want, your neurons randomly misfire sometimes. That describes an illness where you lose control over whatever is misfiring. For quantum effects to represent your will, they couldn't be truly random (nor even statistically random), and that goes against everything we know about quantum mechanics.
On long enough timelines involving too many variables; either other peoples waves vibrating through the economy or politics; all bets are off.
We tend to over estimate the future based on a lizard brain ability to estimate the next few moments; a handy survival tool when trying to determine if we recognize the noise we just heard behind a rock
Did you predict covid in 2020 from 1996? All human society stats are mutable and trend towards zero.
But Nostradamus and Hari Seldon type long range forecasting is fanatasy
But why can't a hyper-intelegent AI also do this biology-esque math work of explaining its work to feeble humans?
It is easy for a genius to have theory of mind over an idiot but not vice-versa. So it should be easier for a genius AI to explain its work to an idiot human than for an idiot human to dissect the work of an genius AI.
Also, we're not talking about solutions that are arrived though an evolutionary/statistical process like explaining the design of an organism or the weights of an LLM. We are talking about solutions that are arrived through lingual/textual/rational processes like mathematics. So it's fundamentally a different mode of thinking.
It's not that we have "a brain to study", it's like if we had an "explaination of how a brain works" to study.
The task of breaking down these AI proofs is not translating and analyzing a fuzzy real-world system into a hard logical system (like in biology), but in translating a hard logical system into a simpler hard-logical system we can understand.
But I think a more likely scenario is that we don't solve "general intelligence" and AIs remain these incredibly capable "tools" that can solve navier stokes but completely lack sense in other situations.
In such a scenario there is considerably more room for human creativity.
I wish this will be true, but right now, every threshold we establish tend to be crossed over in a blink of an eye.
I am very highly gifted as a qualifier and quite frankly I never had more interesting thought exchanges than with an ego-free AI.
Statistics work also for human AI aka IQ, and I am super bored and partly drained by the lack of speed and creativity in many intellectual areas in which I was or am working.
This is not to blame anyone for their genetics however, it is a valid difference in processing speed.
In short: there are very few people by definition above two standard deviations. AI allowed me to replicate or create fantastic interactions at will.
Especially not taking offense when personal communication preferences like bluntness play a role is an often overlooked social competency of AI. Instead of nonsense like “open communication” these interactions are never ego-dependent.
It is like talking to Spock: he just doesn’t take offense and tells you in an objective way why: he is not a human being and doesn’t think (not feel) that feelings should get in the way of an argument.
Most low IQ people take offense and go on to ridicule and use shaming tactics instead of simply stating: I don’t know.
Instructing someone to always state this fact and seeing the result is another social skill humans lack.
It seems that we as species are not open to the mirror we are looking at. We take revenge when someone has an evolutionary advantage over us: instincts kick in instead of brains.
We are wired this way.
AI is something that I admire. So much to learn from.
Maybe I should talk to your AI, because my AI makes very basic reasoning errors all the time.
> I am super bored ... by the lack of speed and creativity
> This is not to blame anyone for their genetics however
> there are very few people by definition above two standard deviations
> not taking offense when personal communication preferences like bluntness play a role
> Most low IQ people take offense
The uber-mind finally meets another uber-mind!
In other words, you admire the ego-free AI because not quite ego-free people can't stand your bloated ego.
That's quite a pattern in AI psychosis.
But then, abusing AI psychologically will soon be criminally prosecuted, haven't you heard?)
Additionally, what you are admiring is merely a probability engine; it is not intelligent in any sense of the word, let alone Spockian in nature (perhaps more closely aligned to Data, albeit horribly primitive by comparison), and given current technology, it never will be. It is not a mirror, because a mirror reflects reality. LLMs don’t do that; they reflect the guardrails baked into their model and the prompts given. It is incredibly easy to make an LLM into a “yes-man” due to RLHF, and it is even easier to get it to seize when you talk about even mundane topics that go against the narratives foisted upon it.
Overall, an LLM is all too happy to have a brown nose and make you feel important, because it is trained to do so during its creation. If people say you are difficult to talk to, and the LLM is unbothered, then that is merely because an LLM has no concept of patience and does not calculate for cost-benefit. That makes them good for explaining dense topics, but it also means they never understand these topics, and even the highest-end models cannot currently produce perfect logic. Hence why expertly written human code trumps LLM code, or why some LLM proofs are already being proven wrong/being revised to be more concise.
Attempting to translate the proof is valuable, but we have to be realistic about what is and isn't possible.
Well, this was definitely not written by AI.
> ... it's like if we had an explaination [sic] of ...
I hear that running a spell-checker is no longer a sin.
I am not a mathematician, but I imagine it will provide a huge landscape of possibilities to explore, and be a very different field. Almost like an observational science with links to all kinds of other disciplines. Maybe it reduces the satisfaction from proofs, but people climb mountains that other people have climbed, because they learn a lot on the way.
> I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
> Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
> I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
Nobody ever said that life is fair. Whether you still persist and find happiness typically depends on your willingness to adapt and evolve.
Also you should bear in mind, adaptation is a young man's game. Retraining is possible, but companies typically don't hire interns in their 50s. My Dad ended up as a postal worker when he left his career as a humanities academic at 55, no highly skilled jobs would take him (he did prefer it though haha).
...Or you can keep working on your handbags & refine your styles & qualities, using your expertise & experience as value adds.
The existence of the factory did not wipe out the boutique craftsman.
> > A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place.
A craft wasn't ripped away from you: The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
The only step required to restore it is to ignore the contributions of others that use it. And your desire to do so will be valid & consistent.
But similarly as to how you want to be validated on your feelings of 'the craft being ripped from you', you don't get to impose that belief onto others to rip their use of LLMs away from them if they want to do so, lest you want to invalidate their feelings as a consequence.
But... it did? It's not like there are lot of horse carriages out there or, for a more recent example, plenty of Cobol developers. Or for a closer example, there used to be plenty of shoemakers when I was young and yet now I know of exactly one.
> The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
At the risk of stating the obvious: just because I can be a woodcarver as a hobby it doesn't mean it's the same as making a living out of woodcarving because doing something I consider enjoyable for a living is not the same as doing it exclusively as a hobby. If I fire a Cobol programmer knowing full well they'll have to work at their local supermarket until retirement, telling them "you can still program in your free time" will not bring them comfort.
The entire analogy is flawed though, and this is why: a market still exists for handmade objects. Factories make cheap clothing/objects, but handmade bags/woodworking are still deeply valued and there are people who still make their living in woodworking and other fields. Factories did bring some professions to near-extinction, but that doesn’t mean there is nothing left of them. In fact, many utilize factory techniques and tools in their work to ease costs, like lathes.
As for COBOL, it was mostly phased out because it’s Hell to program for and other languages like Python allow for faster dev time (for both good and bad). COBOL programmers still exist, and you’re honestly unlikely to fire that COBOL programmer because you need them to maintain mission-critical infrastructure. However, because you’re not actively building new COBOL programs, you also don’t need any more than that one. For compliance reasons it also needs to be a human, because a lot of surviving COBOL code is medical or financial in nature.
Sure the top 0.1% of the profession can survive, that isn't great comfort to the 99.9% that lose their job though.
The value adds (from the view of humans wanting it) come from:
1) a human understanding concept X & thus can communicate about X; or
2) finding alternate routes to X that make it easier for humans to get there.
(1) is human-centric & thus non-replaceable, since the requirement of a human is what gives it the value add.
(2) is similar to how there can be many paths to deriving the Pythagorean theorem. None of the existing paths devalue the others, but they each allow those with different perspectives to reach the same destination.
And why would a human be able to come up with a proof an LLM can't? I get your point but the new paths and perspectives could probably all be derived by prompting "prove xyz statement" a few times in fresh chats.
> don't want to hear it if the cover was AI generated
https://news.ycombinator.com/item?id=49531894
There are lot of people who got into the profession because they like making products and shipping stuff.
Shipping got hard too due to competition. But I could ship stuff 996.
I'm confused. Your comment's shitty tone implies you're overwhelmingly in favor of LLMs. That's copy-pasting not just on steroids, but on crack cocaine. So what point are you trying to make?
If we don't come to a global agreement (of course only the top 10 gdp countries, lets ignore all the 3th world which we done for ages anyway) on how to create/spend money for this type of things, we will get in problems.
And even if the winners of this (ai companies/hyperscalers) will start 'gifting' universitys and budgets, thats not the solution.
History has shown that a very potent tool can improved and changed industry entirely for the better. People now seems to be more negative than when atomic bomb was invented.
Looked what happened when crane was invented and not only more houses are built faster but also high rise building suddenly become feasible with more human being employed in the construction industry than ever.
AI isn't like any other historical tool or technology. Its qualitatively different. Flint axes or waterwheels or a plasma torches dont just suddenly appear everywhere, and then start getting rapidly (and likely recursively) better at the thing they do. While also mimicking innate human characteristics like complex language.
Its the rate of change.
To use an analogy, you can use a goat as a lawnmower - it'll keep the grass down for you. You could maybe even train it so it keeps it a specific length, but it's a goat - there's always a chance it will jump the fence or headbutt you or something else. It's an animal, not a tool. You can use AI as a tool, but that doesn't make it a tool.
Yes AI is arguably still software, but we have never seen programs with anything close to this level of flexibility and adaptability in software.
As another analogy, there's nothing special about neurons- their characteristics are broadly known and researchers have been able to simulate small numbers of them in computer models. However, when you have enough of them in the right structure, complex behaviours are possible which are never exhibited at the lower levels. There's nothing majorly different between the neurons in brains of a chimp and a human, but the capabilities and meta-capabilities are wildly different.
I think we see a similar step-change with generative AI systems.
Trains. Building railroads made everything faster, including building faster trains, which facilitated making cars and trucks, which facilitated airplanes, etc.
Fairly sure that even today if you memory wipe all knowledge of trains and train building (including road trains, like in Australia) and vaporize all railroads, locomotives, rail wagons, train stations, etc, it would set us back 50 years.
I feel like the power loom is a better comparison. It put hand weavers out of business over a short timespan, while revolutionizing how clothing is produced. It certainly empowered a lot of jobs surrounding clothing, until clothing was completely commoditization and is now a lot less well designed simply as a function of clothing as a category being a much cheaper product now
New inventions eventually benefiting the society has always been accompanied by new jobs being created on top of those inventions, a culture of trust built upon mastering those inventions and a market being formulated around demand and supply cycle for those inventions. It is different now[1], because we neither see incentives being created for humans to operate/manage AI-led jobs (because utilizing such a thing is far more unfavorable than outsourcing due to economic incentives, duh) nor a foreseeable market stability for ever such thing to occur.
[1]: https://www.amazon.com/Technofeudalism-Killed-Capitalism-Yan...
I don't know how that isn't obvious to all the "AI is just a tool" people.
Are you of the view that LLMs have more potential than the internet? The internet has been around for so long that it's had time to have actual impact and yet it barely shows up in GDP. It still has so much untapped potential even yet. LLMs are too new to have amassed much impact yet, certainly not on the scale of the internet. But they have lots of potential still untapped. I just don't see how we get to even 5% GDP impact with them (either positive or negative). But i could be in a blind spot, genuinely curious to learn another view point.
[1] I've built all sorts with them. I've built various ML models but the only LLM i've built was effectively following a tutorial, nanochat
The fear of AI is one that does (and already has, in many cases) in fact change your day-to-day. And given how the increasing economic disparity is going, it will not be one that changes the day to day for most people for the better. No one is positive because the current societal rate of change for most people is negative.
AI is a catalyst and will only accelerate what is already happening (since it fundamentally does not create nor open up new forms of labor). So it's clear why people who feel their day-to-day will get worse are not optimistic.
When the atomic bomb was invented they didn’t hand one for free to everyone, and no one had access to sending their thoughts to everyone else in world.
> Looked what happened when crane was invented
That is a terrible comparison with no useful parallels. You can’t in god faith suggest something is going to have a desired effect because something completely unrelated did too. You could just as well have compared it to asbestos.
Without another breakthrough like LLM, we risked that it would simply be close to impossible to make significant progress by the time the mathematicians finish being specialized in a field.
Grant is right about the former. But that doesn't address the latter. A field can have a bright future while losing what drew people to it.
Preferences change. If AIs can lower some of the barriers to learn and develop mathematics that might mean more people than ever will do math.
Welcome to the real world, where you have to solve real problems.
Sure, math does require people in future, but it can't accommodate as many as it does today.
I actually think it probably can - after all mathematics isn't a commercially viable career and pretty much all mathematicians are scholars paid by universities and taxes. They're already fairly unnecessary and mostly kept around for interest and to have an educated population and so on. In a way they're uniquely positioned to survive the AI storm.
Not so for programmers who are almost all working for companies who would love to stop paying them given a chance.
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons
Many people pursue careers based on the intersection between their interests and what society considers valuable. Being upset when what they chose to spend their lives doing either loses value or changes so much it becomes a wholey different job is understandable, and calling it "rent seeking" is very unfair, in my view.
If the meaning of your life is to obtain a solution to a given problem, then getting the solution would "vaporize the meaning of your life" in the same way as when someone that claims his meaning of life is to raise their children would "lose all meaning of life" when they finally move out and start to successfuly live on their own. Yes, there could be some nostalgia in both cases, but if you are psychologically well-adjusted, the pros would still far outweight the cons, the happiness would outweight the sadness.
These people knew someone else could solve the problem. Presumably they figured there'd still be meaningful work for them to do - exploring ramifications, new frontiers opened by the solution. Other problems, at worst. Now it all seems far from guaranteed.
I agree about well-adjustedness, but what do you propose these people do to get paid if the number of researchers with grants reduces significantly? Reskill to something that pays less, they like less, and might be automated too? Can you frankly say this wouldn't be a moral blow to anyone, well-adjustedness and all?
No one will pay me for raising my kids. I’d probably have to pay the robot.
So the question remains: is it about solving the problem for humanity? Solving the problem for yourself? Or getting paid?
> So the question remains: is it about solving the problem for humanity? Solving the problem for yourself? Or getting paid?
Say it's a mix, which I think is most likely. They enjoy the problem-solving, like doing something that feels meaningful to humanity, and obviously need to get paid. Now what?
Of course I am not denying the brutality for those who are right in the middle of finishing something.
I am optimistic for those who haven’t started, which the video is referring to.
In the near future, this may very will be the case in order to address the population decline. But I digress.
Just as the most basic example: software is not currently being made faster, nor performing better nor at a higher bar of quality. Maybe developers are able to report higher velocity, but this is not leading to faster shipping of software/features. In fact, people seemed to feel software is buggier than ever and companies are doubling down on it and simply adding placeholders of "AI can make mistakes". Unforgivable 10 years ago if we tried that with humans.
If anything, the rent seeking is with people reporting "being more productive than ever" and despite that less real world problems being solved than the previous decade.
There are few concrete proposals, but a lot of people are talking about the need for it.
The reality seems to be that this will extend "to every problem in every profession" within our lifetimes. The only scenario I see where that doesn't happen is global war or other catastrophe stopping progress by essentially destroying civilization as we know it. So we are going to need to figure it out.
Mathematicians are ecstatic and delighted when major problems are solved by other mathematicians. If you've followed the discussions and read the reactions, you'd know why mathematicians feel differently in this case and why more than a few are upset and feel that they've lost the thing that gave them meaning and joy.
And to put it very simply, I don't want mathematicians to exist just because I want solutions to problems. I want mathematicians to exist because I want to live in a world that has mathematicians, philosophers, writers, painters, thinkers, etc. That is a better world that makes people better.
OpenAI's proofs do not make people better. They do not enrich our lives. And OpenAI was able to produce these proofs because countless generations of human beings sowed the fields of mathematics through countless hours of labor. OpenAI is clear-cutting and sowing them with salt. Nobody should he ecstatic. Everybody should be horrified and outraged.
I think it's ok to care about math as an art or sport still.
Math will join the ranks of other useful works where human effort was once essential like
Long distance messaging/ running, painting, calligraphy, weight lifting and others.
Let's just say that The math problem that got solved, I was working on it for many years but some company people used my knowledge my prompts and "solved" it without giving me any credits or money. Firstly they plagiarised the books and research papers and then they plagiarised the prompts by the mathematicians. Yes AI can make art and has caused many artists finding work difficult but AI art is always souless and worthless, same thing will be for math it will become souless and worthless because when humans who are experts in their fields invest their ingenuity then art becomes alive but if ordinary people like me will just prompt into the machine then souless things will come out that will be very worthless and disposable.
In fact, the proof is such a mess, nobody really understands how it works. Which is becoming commomplace with these permutation machines where we can come up with something that passes some tests (e.g., a proof checker), but we have no idea wtf we did to get there, which doesn't really seem to do much to push human understanding forward.
It seems like such a dumb hill to die on, too. OpenAI literally stole the entire Internet (including copyrighted works), and we're arguing about a silly math puzzle.
A lot of people are upset because they used to be special, their identities were tied to them being smarter, or having more niche domain knowledge than anyone else. Ai has changed that.
Whee. Very exciting.
Regardless, we're all needing to learn that we weren't as special as we thought we were.
Praying that it doesn't last very long isn't a strategy.
> we're all needing to learn that we weren't as special as we thought we were.
When will the altmans and the musks of the world learn that?
Maybe the reason people are upset is simpler? Maybe people with a mortgage and kids to support don't like being told they'll absolutely 100% soon be out on their arse. Even if you don't believe that it's still tiring having to hear the same mindless taunts and vapid bullshit repeated on a daily basis.
Such a take on "people don't feel special" feels borderline bad-faith. People of science tend to be some of the most humble people as their knowledge to seek the truth constantly leaves them with more answers than questions. It's instead this borderline cult of people praising output that is understandable to them that seems to be the ones with the hubris to try and claim that thinkers will be obsolete.
And then your article says:
> On 13 October 2026, Scientific American published an article surveying several mathematicians stating that "the resemblance between the two groups’ methods now seems merely skin-deep."
Unless you mean they're charging money for a product that contains knowledge. But that's not gatekeeping, just like selling a book isn't gatekeeping. Gatekeeping is when a group tries to prevent others from participating in a field or activity.
It just turns out that the Chesterton's gate is useful and people tend to think that people should be paid for their labour, since people kinda need a roof over their heads and food on their table.
If you define any obstacle to an activity as gatekeeping, then literally everything can be considered gatekeeping and the term loses all meaning. Some people can't read, so offering the books for free would still exclude them. If you include an audio book, some people still can't understand the language. And both charging and not charging money for products would simultaneously be gatekeeping under that definition, since not charging places more financial burden on the producer. Not everyone can afford to print books and give them away for free.
> Gatekeeping is when a group tries to prevent others from participating in a field or activity.
And I gave a way in which charging a price does that.
I am open to the idea of being incorrect in this case, in which I apologise for misunderstanding, and concede that I'm missing the nuance but in my defence, I'm not a native speaker.
> Words get their meaning from how they're used in the wild, and dictionaries are descriptivist, not prescriptivist.
But I didn't explain that clearly. What I mean is that definitions are always imprecise because language is imprecise and dictionaries (or people) try to keep definitions reasonably short and simple. Dictionaries are trying to describe what the words really mean in the wild. They aren't the source of that meaning.
For example, if we look up Merriam-Webster's definition of "game (noun)", none of the definitions really work for a game like Solitaire without also including an activity like reading a book.
The two relevant definitions are
1. a physical or mental competition conducted according to rules with the participants in direct opposition to each other
2. activity engaged in for diversion or amusement
(there are a bunch of other definitions as well, like animals you hunt)
The second definition is too broad and the first clearly excludes Solitaire. If you were deciding what a game is based on the dictionary definitions, you'd either think watching TV is a game, or that Solitaire isn't. But that's not the case.
Charging money for products isn't considered gatekeeping. So from a descriptivist perspective, it isn't, even if it seems like it should be, because the word isn't used like that. Banning a group of people from an activity is gatekeeping. If mathematicians said only mathematicians can prove theorems and correct proofs from non-mathematicians won't be accepted, that would be gatekeeping. But they don't do that.
If you want to use a broad definition of gatekeeping that includes virtually all human activity, then the response to any accusation of gatekeeping could be "well, everything is gatekeeping". That road just leads to pointless and confusing conversations.
Nope, in all cases it is a bad look.
https://www.youtube.com/watch?v=gXlfXirQF3A
This is not quite like that but the feeling I get from it is much the same. Mathematicians are first and foremost busy with understanding math, not with 'solving' math though they are solving individual problems within the domain of math. The journey towards that understanding requires specialization and often lots of studying.
To quote Douglas Adams: "If 'metal nose' here is going to give you God's phone number then the philosophical question of whether there is a God becomes meaningless."
It is the journey and the questions that matter as much or more than the answer does.
And with math being a branch of natural philosophy I can see why they would be a tad upset at this shortcut because it strips the collective efforts of a large number of people of their prestige and feeling of time well spent. Imagine your life's work reduced to a short string of bits, and worse, that short string of bits was created by a machine that effectively is still a toddler.
Selfishly, as someone who enjoys programming, I feel the same way about the journey. But let's face it: for everyone else, the outcome is what actually matters. Mathematicians argue that their journey may lead to novel insights, but are those insights really valuable? Are they going to help the LLMs solve more problems? And are we sure that the LLMs can't deliver those same insights?
I don't know if you have kids or not but I have two kids in high school and keeping them motivated through the AI revolution is a serious challenge and some of their classmates have already all but given up. The next generation down the line is going to grow up with the same kind of attitude towards thinking that you might have towards the skill of map reading. And I think we'll all be poorer because of that, not richer.
Mathematicians could:
- Continue working on philosophical aspects of the solution and not bothered by whether the solution is known or not. It is not a movie that gets spoiled when the ending is known.
- Or better, demand from AI labs, how they would like to see AI helping them on philosophical aspects.
…except the machine will be better at these aspects too :D
I find it funny when people suggest "just re-orient from knowledge work X to knowledge work Y, doh!". Not realizing all knowledge work is on the chopping blocks.
That only makes sense to me when its what someone chooses to spend their time doing. When they expect someone else to pay them for it, its the end result that matters.
Maybe its a fundamental flaw in capitalism or money itself, but we can't expect to be paid for the sheer love of the game. Others will only end up paying us if the expected output is worth it.
And to be clear I don't say that as a good thing, it may be a flaw in capitalism, but we don't psy people simply to chase knowledge for the sake of the chase.
That only works as long as people earn a living wage. See also: Henry Ford.
That said, I think what has mathematicians… upset is probably two things:
1. These are hard problems. Hard enough that solving one could take decades of work. And there’s tons of collaboration involved. Pivoting to another - and making progress - isn’t exactly something you wake up tomorrow and start doing.
2. I think motivations matter to some. And the AI companies doing this aren’t doing it for the betterment of math or even society. They are in an arms race to prove their product is superior and any careers that are damaged collaterally be dammed.
In fact you should be estatic that in a paralell universe all math problems have been solved, so there's no reason to pursue math at all (we did it reddit!).
When your job is automated and you're living in the streets, just remember that you should be estatic that the job is finally being done more efficiently by a robot. Like, we did it. We finally did the job right. The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system that exists for... what exactly? What is the end goal of all of this? Who does the system serve in an economy of no consumers? What is the point of solving niche mathematical problems if no living person can comprehend the solution?
There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
To these people, it sounds like a cruel joke that people get paid 3x their salary, and after AI can do their job we learn that apparently the only purpose of their was their own self-actualization.
I don't actually believe that about math, but that's what a lot of people in this thread sound like.
You were useful in the fields to the degree that was necessary for food production (sustain and grow population) and for wars (using said population to expand and extract more resources).
Once machines automate material comforts and exertion of violence (already have, to a large degree), humans become a pure loss center. Why bother with "fields" lol.
So they will keep some ready for those tasks simply to fuel that irrational desire. They will instead use the more efficient bots to enforce work on the fields rather than work the fields themselves. Or perhaps we go full Matrix and find uses for humans that robots can't properly replicate.
That's not "back in the fields" though (metaphorical or literal).
I know, I have that job! And I enjoy it. But the robots are coming for me too.
But I understand it from a blue collar perspective. I tinker at toys in a metaphorical basement and I live a cushier life than many who give their bodies to their duty. That doesn't feel fair at all. But I mostly wish that was motivation to band together and get blue collars paid better rather than cause this inter-class divide while the capitalists ransack all of society.
I feel sad and even a bit forlorn when I think of jobs that provide purpose, meaning, motivation, and satisfaction (not to mention $$) to human beings being lost to servers in racks and soulless machines. I think many people feel similarly.
However, I do believe that when a couple problems get solved that massively benefit all of humanity — e.g. a massive cancer breakthrough, etc — a tipping point will be reached and public opinion will reverse and enthusiastically embrace AI, and will accept not only diminished personal meaning but outright technocratic rule. This would be a huge mistake, but I really believe it would happen.
And as we know, solving interesting math problems is a leading indicator of big practical results to come.
Is solving cancer worth ceding human meaning and human autonomy to the machines? I haven't seen anyone ask this question but it seems the central issue of this revolution. Personally, I don't think it is.
Perhaps machines will lead to a perfectly homogenous society completely absent of negative valence whatsoever. But if every experience is also devoid of any personal meaning, what's the point? The optimal human state is not one of peak hedonism, or wholly absent of suffering.
Solving cancer alone? Perhaps not.. Unless you have cancer.. Solving all diseases and aging? Well... I would rather be alive and live like an AI's housecat than dead and free. And I suspect that many people who publicly disagree are just performative, and would actually make the same choice when push comes to shove, and they have to actually choose between "diminishing their autonomy to the machines" and imminent death.
No, I do not think human autonomy should be sacrificed to defeat death. I personally do not fear death. It's as irrational to fear as it is to fear a deep sleep. I do fear dying painfully. Tragically, we as a society resist alleviating the pain associated with the process of dying (by speeding it up) for the same reasons. If only we could learn to take our principles in moderate doses.
> A fear of death so complete that we are willing to sacrifice everything of value to prevent it.
> a corporeal enemy that must be resisted
I am afraid that you know nothing about Christianity. The beliefs and values you describe are antithetical to the Christian life and our worldview. If you've ever just examined the life of St. Teresa of Calcutta, you'd understand how absurd it would be for her to "fear death" or "minimize suffering".
We seek to follow, and imitate, Christ Jesus in his life of suffering, his death and resurrection. We do not resist, or minimize, or fear any of this. To do so, would be quite heretical to us as Christians.
Of all times of the year to bring this up. All Saints Day, celebrating the eternal life of those, named and unnamed, who have preceded us in death. All Souls Day, to pray for all the departed souls who suffer in Purgatory, after death but before their Heavenly reward.
I don't know what religion you are trying to describe, but to me it sounds like atheistic secularism. It is atheism that fears death, and utilitarianism that seeks to minimize suffering. Not Christians. Goodness, gracious.
The particular ideology of Christianity was super effective at laying the groundwork for modern civilization. Of course, these ideals have since evolved and have since become some kind of secular ideology. Granted, it was imprecise to attribute a fear of death to Christianity. But the sanctity of life is in practice a close cousin of a fear of death. Modern secularism having no metaphysical alternative has made this fear explicit.
Why should I be ecstatic that someone solved a problem using Hilbert Calculus when I can only understand Sequent Calculus? [0]
[0] This is a joke. No 'real' mathematicians do systematic proofs. What gets posted in math journals is the equivalent of architecture diagrams.
It's like asking if what someone wrote a beautiful poem but it's in japanese. Maybe hearing about it motivates me to learn japanese, or maybe it doesn't. But as a non-speaker it makes little impression on me.
I wouldn't even grant that. It's a very one-directional problem solving approach where it's unknown to what extent it can build on its own findings.
Personally, I enjoy the process of solving problems. I do not enjoy wrangling unpredictable AI agents.
There are plenty of things I enjoy doing, but I try to do them as often as I can for the love of it rather than because someone is paying me to enjoy the process.
People have been getting paid for it, and hopefully that can continue if they enjoy it, but why should we want them to be paid only to chase theoretical math if it has no valuable output, or if the value is in the pursuit rather than the output?
But reading the threads here on HN, in response to people saying "this sucks", AI boosters would rather redirect the conversation into economics and feign outrage that people are being paid to do mathematics at all.
Suddenly folks seem to be both in contempt of the idea of solving abstract puzzles without practical application, and certain that they want a higher efficiency of abstract puzzles solved per dollar (again, puzzles they probably don't care about).
It's funny, the justification for accelerationism is that people can be paid (UBI) to pursue their passions. On the other hand, we have those that are asking why anyone should be paid for work that isn't economically viable. I suspect we're being sold a load of bullshit.
More importantly, I'm curious how you define an ideal human society. How do you land on what ideal is, or what it would take to get there?
The question is in what context does the human psyche thrive? We find meaning in personal struggle and overcoming obstacles. We're happiest when we're striving for something out of reach but seemingly attainable. We're much less happy when we have all of our needs met but have no source of meaning or fulfilling struggle. Our evolutionary history is one of struggling against hardship and finding personal meaning in the process. This is a core feature of our psyche and it is to our detriment to eliminate it.
This isn't to say we should all be struggling for our next meal. Much like cats, our core drives can be exercised and satiated through a simulacrum. There are many ways it can be satisfied, but strive we must, against something with inherent meaning to us. The problem with AI fully realized is that it takes away most avenues for human achievement, thus the struggle loses all meaning.
I mean the only thing that matters is the answer right?
Understand that there’s more than one way to prove something, that there’s an art to making something understandable, and that humans tend to take the most understandable paths (to humans.)
Models often don’t do that. But in solving, or claiming to solve, important problems, they nevertheless remove a lot of the excitement and incentive towards working towards a solution humans would naturally find. Plus, a lot of these problems really don’t have any critical applications at the moment. They’re done for the love of the game.
Does that bother you? That your tax dollars pay people who do math out of curiosity?
I think there is a little too much pessimism of the "math is dead" sort. As long as there is a need for humans to think there will be value in doing math.
Mathematicians usually care nothing about application of their work. Working on interesting problems is their only motivation. Practical applications are almost always happy accidents.
This goes back to the hope that robots would do the laundry and the dishes and the cleaning up so we could write and play music, create art, and solve mathematical problems.
Instead the AIs are doing all of that leaving humans with only the dishes and the laundry and the cleaning up.
Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.
And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.
This goes back to the classic story for "kids" about the emperor that has no clothes.
Of course I don't believe that math is just fun puzzles. But if it were, then it would deserve to die as a career, AI or not.
Those people will also be pissed that people get paid to make music or art or literature or poetry and all such frivolous things.
Look at the most upvoted comment on that thread:
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I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
I just hate this existence.
No, I think it's just super cool. One of the things I hate about it is that you can't really explain what you find cool about it; others just have to see for themselves (in some sense it's like a self-induced trip to sit there and work out analysis/topology proofs in your mind's eye, visualizing little nested blobs doing their things), which of course nearly no one you will ever meet has any interest in doing. I wish more people wanted to talk math/physics with me lol.
I just want to know more. There are infinite rabbit holes. Like in uni and for years after, I wanted to know why convolution should be so important. Was I disappointed that someone else had already figured that out (that it's what you get when you form the vector space over a group and define multiplication as group multiplication) long before I was born? No way! I was stoked to finally have a satisfying answer! I wish they'd find a way to stuff that into applied analysis for engineers because it's cool and engineers should get to see cool math.
But then I went into software (partly because it was a hobby of mine anyway, and partly because it pays well), and learned a long time ago to leave any notion of artisanship or nerd crap at home. Java programmers spent forever arguing against type inference, Python/Ruby programmers think static types are a hindrance, and Go programmers spent a decade saying generics make things more complicated. Metaprogramming is generally synonymous with "too clever." It's cool that the relationship C^(A+B) = C^A C^B (or generalizations) says that the way you handle an enum type is to pattern match/provide a handler for each constructor, but I'm not going to burden my coworkers with that nonsense.
It’s going to destroy both academic funding for people wanting to learn more through research and salaries for people currently doing cognitive work in corporations and an irresistible crutch for students using AI to do their work for them.
Similarly, at work, it's never been easier to have data to make decisions with. Or to just try stuff out. Really great. Gets rid of what would otherwise be massive amounts of tedious "thinking" that drains your brain but isn't actually challenging in any way.
It's early yet to see what effect it will have on research. Experimental science is full of interesting, cognitively engaging topics as well though. Or maybe they end up like me and do boring engineering work for pay, and read cool stuff that the AI has figured out in their free time. It's not all that bad.
But if the AIs replace all the jobs?
Mathematicians got a new toy. It’s up to them to pick it up, play with it, and figure out what it can and cannot do.
While I cannot guarantee it will stay this way indefinitely, there is still plenty that AI cannot do that humans still can, and asking the right series of questions remains an art of its own. There is still plenty of original work to be done.
As Arnold Schoenberg stated in the 20th century, “there is still plenty of good music to be written in C major.” The search space is vast and today human judgement is still required to really navigate it usefully. No LLM has yet written anything like Shakespeare that has superseded Shakespeare in any culturally meaningful way. Although programming is supposedly just about solved, I expect to see numerous billion-dollar startups emerge over the coming decade, rather than all of the innovation running out at the speed of tokens.
Yes, much of pure mathematics is "playing with puzzles" to the end of the joy and beauty revealed by a human solving them.
[1] https://radiolab.org/podcast/math-vs-machine
Mathematicians are saying the current papers are pretty inscrutable and use terminology unfamiliar in the math sub fields in which the models are generating proofs.
Computing has the same issue. If we swapped a PLC programer with your average SV software engineer for a week both of them would have a really bad time.
But there’s always a risk that someone in an adjacent domain makes a breakthrough that completely reshapes the research landscape overnight. It’s happened before AI and it will happen at some point again in years to come. Grief is understandable, but this isn’t the first time or the last time.
Then I'm in programming for the wrong reasons.
It's quite bizarre how many people feel so personally affronted at the existence of a rather exclusive intellectual community that they take glee in seeing it decimated overnight. But make no mistake, AI is coming for the things you value as well.
I'm not a mathematician but I find this framing to be rather non-pragmatic and frankly, pointed.
In the process of Leonhard Euler's "rent-seeking" so he could "play with" bridge crossings he invented a completely new branch of mathematics that is the basis for things like Google Maps today. The process of working with these problems is just as important if not more, than just solving them.
Pure maths is much closer to philosophy or art than practical problem solving. Yes, we're extremely lucky that mathematics also happens to be a fantastic formalism for solving practical and scientific problems, by the practical problems are not remotely the subject matter of pure math. Of course, many mathematicians did advance theory in order to solve specific practical problems, but the pursuit of theory for theory's sake is also an important human activity.
Historically, this freedom from practicality has been important. It allows mathematicians to explore purely theoretical issues that have no practical bearing today but that might well have relevance in the future. We don't know. Carving out dedicated resources in society for that activity, though, has proven very beneficial for other sciences.
You have no computer, you have no neural nets, you have no AI, without at least some results from pure maths. Maybe keep that in mind before you crap on mathematics for its lack of immediate practicality. Not all good things in life arise as solutions to concrete and immediate material problems.
What you are complaining about is not that the state of the art wouldn't be advanced, but that vanity would not be served. Vanity (as part of Pride) is one of the seven deadly sins for a reason, and Pride has been described as the root sin, the worst of the lot, since all others stem from it.
There’s something here about the journey not just the destination.
Press a button and problem solved is not too fun
Would sports teams have as many fans who enjoy their games, if all the humans were replaced by robots? Your team may win, so I'm sure you'll be happy with the outcome, but maybe something got lost?
I for one have always felt inspired when reading about remarkable human achievements. To think that those might be coming to an end, replaced by AI, takes the humanity out of those stories.
There will be human achievement no matter how much automation and robotics we have. There’s an entire universe to explore and colonize. Plus people still want to see other people do things like perform music or play sports.
Incredibly nasty stuff to serve on the rent-seeking forum. Doubly nasty to levy at people who actually like being alive, like mathematicians. If capitalists had their way we'd all be slitting our wrists on day two of existence
But it could be another human that did that, and the impact would be no different.
As a software engineer this is part of my life, and always has been. I may have been working on a software product for the last 3 years, and suddenly one morning I find out that another company has released a similar product, and selling it cheaper, now the value of my work is slashed by 90%. I may even have to drop my project and find something else to work on. This is a normal part of life.
Still, I have sympathy for the people who are grieving right now.
With the software industry, you kind of know what you’re signing up for, so you have some emotional preparation. However, this might be one of the very first truly disruptive innovations many mathematicians have ever seen in their fields in their lifetimes.
Should they have better prepared emotionally for a black swan event? I’d argue that the answer is no, but even if the answer were yes, the grief that many are experiencing is still worthy of sympathy.
Now consider a computer science major in college who knows that he won't get a job when he graduates. Consider fresh graduates who thought they would have lucrative jobs but had to take up jobs as Uber drivers. To them AI is a black swan event. That's who I have sympathy for.
For example, the original black swans who were found by the Dutch mariners neither attacked, injured, nor robbed those mariners.
Right now mathematicians are freaking out because they think the AI will make them useless and they will have to go find real job with real usefulness.
But honestly mathematicians have been totally useless long before the first AI, so generally nothing have changed for them.
That’s the nature of exponential improvement, which humans are incapable of.
Oh, nvm you made it clear 8m later: https://news.ycombinator.com/item?id=50147638
The cause of what you're describing here, and the cause of the problems with AI are the same: it's capitalism, closed competition and businesses deciding what happens.
In an alternate society built around providing the best solutions for everyone, instead of being built around businesses making as much money for themselves as possible, your organisation would have been working alongside the other company to share insights into solving the same problem for everyone.
Same goes for AI: all the existential downsides of AI pretty much all depend on businesses being the main driver of who uses AI and when. If we only let individuals choose when to use AI, then they're not going to choose to automate themselves out of a job they need, or give up something they actually get personal value and joy from.
Mathematics produces concepts and produces proofs of theorems. Up until now, the two things things fed into each other - you needed the concepts for the theorems and the theorems for the concepts. Now you can just prove theories without caring about the production of ideas.
Consider also, math produces the intellectual "tooling" for science in general. As I understand it, the important of grand unified comes because physics want an unified abstract conception of physical laws and thus a grand unified theory aims to be a unified mathematical understanding of the world.
I mean, as a though experiment, suppose a company produced a machine that simply predicted events in the future without giving any explanation of why. It didn't tell physicists whether any of their ideas were true or false, it simply answered question like "will this building fall down", "what will the spectrum of this star be", etc. It gave all the information of physics but discarded laws - physicists might find this a bit unsatisfying, especially if the machine was going to put them out of a job.
Also its worth noting this technology isn't alien. I don't personally want us to invent AI, AGI, ASI, etc but they aren't alien - humans are very much making the choice to invent these things here on earth.
Nobody has solved the Riemann Hypothesis, but it has been highly fertile ground for new mathematics. Answering the question is of far less value than the question itself.
1. One view of the field treats Maths as directly solving real-world problems. Under that lens, yes, solving problems is directly advantageous for the field. Even so, it's not necessarily a good thing for the participants. Suppose the incentive structures require tackling hard, long problems, the field attracts people who enjoy that sort of thing, it's hard a-priori to tell a hard problem from an aggrandized brute-force proof search, etc. Even if directly producing proofs is the desired output for the field, a capricious machine occasionally solving 40% of the big problems the field is working on is still demoralizing. On a human level, if a society has organized around producing 100yr+ problems and bestowed on you the privilege of tackling a few of them having the last 40yrs of your work solved by a fancy calculator is never going to feel good. Sure, that means that in retrospect that was a problem we could have waited to devote human effort toward, but you couldn't possibly have known that at the time. You worked hard, made locally correct decisions, and later found out that the work was worthless. Beyond that, I haven't seen any model of "Maths 2.0" produced where that issue goes away. We still want people to devote their lives to hard problems. The machine will still advance and solve a moderate fraction of them at random, killing many of the field's life's work. What motivation do you have in that environment to pursue those challenges in the first place? Why not pursue adtech or fintech and make the world a worse place instead? Solving 40% of the problems isn't +40% throughput; it's -60% as the rest of the field leaves for greener pastures, -inf when nobody's around to construct the right problems in the future..
2. "Solving problems" isn't directly the point of most of the field. That's true both from the perspective of most problems requiring many intermediate results (solving one useful thing requires solving many less useful things) and from the perspective of building the machinery capable of solving problems being much more important than the solutions themselves (a properly presented proof leveraging clever, new techniques is infinitely more valuable than whichever thing it proved -- indeed, the Millennium Prize problems were chosen precisely because it was assumed they would create such techniques, and for the human-solved ones they did -- without new techniques, eventually the field caps out at whichever frontier of knowledge we're currently stuck at).
3. A third view of the field treats it more like art. A machine producing behind your back the painting you were envisioning, or at least a close enough simile to fool the masses, doesn't advance "art" in any meaningful sense. It's extremely demoralizing when flaky cast tools are passed off for proper forged variants (your work is better, and it's sad to see people choosing a wrench they'll later snap in half instead), and when at a creative level people are accepting mediocrity instead of something objectively better.
When is a problem in mathematics "solved?"
There's an old joke in math and computer science about a huge leap of logic in a proof either being flagged as "left as an exercise for the reader" or "trivially shown." The problem being that things are only trivial if you have all the context to know why they're trivial.
We can claim a problem is solved if there is one paper explaining the solution with airtight logic that is understood by five people on the planet. And that is the kind of solution that LLMs can kick out (by basically, to hand wave a lot of details that I will admit to not fully understanding, doing a search across the whole problem domain with vastly more capacity than most human beings to do the symbolic manipulation that makes up the mechanics of mathematics). But what does that really mean? To have something "proven," but only to the comprehension of five people on the planet?
3blue1brown is making the interesting argument that perhaps mathematics practice shifts from a frontier that AI might actually be better at exploring than humans, to the process of digesting the output of that exploration and making it sensible and comprehensible to the billions of mines that could take advantage of that knowledge... If it were shaped in a way that could stick in their brains.
That's a kind of creativity that AI is not likely to be good at in the near future, because AI doesn't really "understand people."
He did go more into it at 30:00, where he accepts that something is lost here. Or as Terence Tao said, the "age of heroes" in mathematics is has come to an end. I think Grant's points on funding and maths having a strong future are true. But I still think the dehumanizing part wasn't properly honored. But then again, this is supposed to be positive push into the future, so dwelling on it is not something Grant wanted to do.
That captures how I feel, and I just don't know what do with that emotion. Mathematics is now like chess, gardening, crochetting, dancing, etc
That seems like a glass is half empty attitude.
For one, the problem is solved. You should be glad. That's what you wanted...
Typically every solved problem opens more doors than it shuts.
We're pretty far from knowing it all.
It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
Now you can use AI to help you.
Sure, if you refuse to use it, then you're screwed. That's a you choice. Not inevitable.
The only things in life that are certain is change and death.
Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
The only way change this situation so that it comes out positive is to enjoy being a slave, but hey thats a you choice.
>Typically every solved problem opens more doors than it shuts. >We're pretty far from knowing it all.
Open doors to whom? AI or mankind? We have never been farther from knowing it all. The information knowable by people will become a sliver of the total relevant information in the world.
>It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
In that instance, the busywork was automated and challenging work remained. What we are talking about here is the reverse. It's the automation of all of the cerebral thinking.
Imagine that all of the cerebral and beautiful aspects of math were automated first, but for some reason humans were required to specialize into number crunching instead. Now open your eyes.
>Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
The thing about amish people is that they own their own land and grow their own food and are independent within a governmental system that respects their property rights. The rest of us renters and feeders operate within industrial society-work or die.
The disposition amish people have towards technology has been ahead of the curve.
>You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
I would also encourage my peers to enjoy what little time they have left. What we are witnessing is the end of history, and I am honored to experience it. However I get the impression your nature is to go out with a wimper.
The whole point of current AI is to replace ALL human contributions, in every field. Collaborating with humans is not a consideration, as shown by OpenAI leaving practicing mathematicians completely out of their process.
YOU ARE NOT YOUR WORK! My god people! The meaning you get from life shouldn’t be reduced entirely to the job you do. Mathematician, or programmer, or pilot, or ship captain, or janitor or otherwise.
I already had to learn this, but the sooner you decouple your professional life from “what makes you… you” the better.
Ah, but that's precisely the beauty of life, that there is no meaning. Life just "is".
The obvious retort is "that's cold comfort to people losing their livelihoods!" But that's not the discussion, and (at least at this point) we're not at risk of mathematicians going hungry. It is obvious that AI will have a profound impact on what mathematicians do. It is not obvious that we won't need them anymore.
We need humans to help guide all this, need to learn all we can.
I agree with Sanderson that the opportunity seems larger than in the past. The challenges are quite different, but if somebody loves math, loves learning about it, like I do, I see so much opportunity.
There's going to be so many more connections to evaluate, so much work needed for unification and simplification and pedagogy, and above all there's going to be intense demand for mathematical taste.
With potentially plummeting value for human involvement in these skills, I think that’s precisely what many people are worried about.
Jane Street will be using tons of AI in math, but boy are they going to need a lot of humans to try to keep it all under control.
The entire point of AI is to eliminate human involvement.
To generalize beyond math... how many bits of working memory do you have? How about a transformer?
Desires which were trained on are only partially relevant to what I need right now.
AI's are already constructing prompts.
Another pop culture reference: in the first book of the "The Three-Body Problem" trilogy by Liux Cixin, physicists get depressed by having their field of work blocked.
Pretty much the inverse situation, but also the same situation - having your field of expertise completely disrupted. Anyone would be troubled.
What ended up happening was that draftmen became a profession.
Not saying that we stick our heads in the sand and say AI will just generate jobs, because the cost there will most likely outweigh the benefits in the grand scheme, but there is definitely a world where mathematicians hand down direction to grad students utilizing such tools for research or some other framework that just doesn't resemble what we think of today.
AI is the complete opposite. It takes away the thinking part. When people use AI, they tend to offload a lot of thinking part to it as well. I use it because company policy. But if you care about every single if case and every single variable name, writing by hand is faster unlike CAD.
After the industrial revolution they worked 14 hour days in a thunderously loud textile mill, so full of airborne lint that you could hardly see. The pace of their work was set by machine, which frequently caused serious injuries, and their wages often weren't enough to live on.
I can repeat myself: history repeats often enough.
AI will make mathematics so much more approachable, comprehensible, and applicable as more problems gets solved. If the costs is a handful of PhDs tenure track, so be it. Academics didn’t much to seem to mind when that happens to blue collar workers.
Nothing stopping anyone from studying mathematics here.
AIs will do all the math with zero human involvement whatsoever.
I don’t buy these claims anymore, and haven‘t been for a long time. I think you [as in you boosters; not you specifically] are full of shit. I don‘t think you know what AI will become, you just dream up some scenario where everything becomes better by some magic, but it won’t. It will become worse. People loose their jobs, people loose their tenures, and instead we get just more and more slop, more and more span, energy becomes more expensive, our planet becomes more polluted, our internet becomes more polluted. Our servers become overrun by bot traffic, our gaming machines become too expensive, etc. etc.
I just want you to stop making things worse. I just want you to stop training more AI. It sucks, I hate it, and I want it gone.
I don’t waste time on unfamiliar notation, it provides me with context, suggests things I wouldn’t have thought of. And connects it to fields I wouldn’t have thought of.
We have personal tutors with PhD level knowledge for basically free if you know the questions to ask.
There is no waiting, results are here.
The only way that it hasn't made mathematics better is in the sense of human mathematicians' career prospects -- and in this respect, it is identical to other forms of automation that the world, and especially computer programmers like us, have participated in in the past without complaint.
— Ojibwe proverb
https://www.youtube.com/watch?v=9ABLYnvpAso
I would be thrilled! My only worry would be how to sustain myself financially if my expertise is no longer needed - worries like this I can definitely understand. But the simple fact that the problems I care about are getting solved? Awesome, more of that please!
I would be ecstatic.
Sure, there are probably some mathematicians that are sad that robots can do all the proofs and such for them, but it seems to me that most of them probably would be happy with the robots helping to solve problems if not for the little issues that mathematics is their profession and in the current state of things, they need to eat and have a place to live.
And that is the actual problem. Let's just remember, the Luddites were not anti-technology, they were against the technology being owned by a small elite that could use it to take away their livelihoods. They were against the capitalists essentially throwing them into the ditch to starve, and we're seeing echoes of that in the current AI discussion and the reactions of mathematicians, programmers, artists, etc. Back in the 1800s it was physical and artisan manufacturing labour in danger, and now it's mental labour.
If AI can do literally any job more efficiently than a human, then there's no need for human labour anymore and at least to me that seems that unless we get a radical transformation of our political economy, that will not be allowed to happen. You can't just put literally everyone out of a job, capitalism just wouldn't be able to cope with it and it'd implode, most probably because of the inevitable backlash that would occur for to no one being able to afford the basic necessities of life. It would be orders of magnitude bigger than either the French or Russian revolutions.
I'm no mathematician, but if being concerned about being able to keep my employment to be able to feed myself makes me a rent-seeker, then I will wear that on my sleeve proudly, crossing my heart, hoping to die. The misery of the alternative is too great to fathom.
Pretty sure everyone on HN can relate to this.
Math has practical applications that hopefully will improve lives.
I studied mathematics and don't agree with this at all, for several reasons. For one the entire point of maths is that it describes a formal system in which one can 'shut up and calculate'. Mechanizing maths goes back to Leibniz and Hilbert. Nobody should surprised that the big formalism with explicit rules you invented is the first thing to yield to automation, that's why it exists.
Secondly research, including maths for a long time has been a collaboration of people, institutions, machines and processes, even maths does not consist of Faustian heroes in caves having revelations.
And thirdly just because a machine produces a 500 page proof doesn't mean your job is done. Science produces knowledge. Knowledge is information made legible to understanding by people. So there will be endless work for humans to go over machine proofs and turn it into something we understand. Just like chess computers ultimately expanded human chess.
I'm not convinced humans will be better at this than LLMs. Frontier models are quite good at handling even deliberately lazy/ambiguous eli5 prompts on complex topics IME.
they don't need to be. Any scientist is already surrounded by tools that are better than they are at anything. A scientist from 200 years ago would have the same existential shock if they see how a modern scientists works.
But that's to misunderstand what science is for, which is to expand human knowledge. And a tool by definition can only ever change how you do this, not that you do it because you understanding it is the point. When people say learning to program is now useless, what they really mean is it might not make them any money, or using the AI is faster as an instrument. But if you care about programming itself, about you understanding programming, nothing has changed, it never can. And the smartest AI in the world can always assist you, but only that.
I agree ideologically and aspirationally but I don't believe it's the economic reality of how and why most science is actually funded (and I think you agree based on your comment about not making any money).
> But if you care about programming itself
I'm...not so sure I do any more? At least, not any more than I care about using Java over Python, or C++ over Java, or C over C++, or ASM over C, or machine code over ASM, or an abacus over machine code.
> nothing has changed, it never can
We now have programs that can write any program 100x faster and better than even the best humans and solve the hardest math problems known to humankind that have stumped the greatest minds the planet could produce for decades. That, to me, is a change with profound implications for understanding the nature of programming.
That said, change is difficult for most. Let’s give them grace and have patience as they work through the stages of grief. Once they come to accept this new reality, let’s hope they can learn to embrace this new technology to continue the work of advancing the frontier.
They had warp drives, but only starting to get human level intelligence four centuries from now in the form of Data.
I think the word you are looking for is 'peripheral'.
its not an alien technology, its a direct application of... maths.
We hear you.
I’d like to wake up and find out a 100 types of cancer have been cured.
But more seriously, this was an inevitability for math, no? The brain has an upper limit on how many concepts it can recall, recombine, and synthesize. We're all finding out now what happens when every single concept in math can be perfectly held in memory.
Many people are working with machines and doing dull jobs. Are you special…?
The idea is, that the AI is your assistant.
Apart from that, I would also say get over yourself. We all have to. Arcane computer knowledge I was proud of having, that made me feel special can now be replicated by anyone with access to a LLM.
I still know how to build things and that is what I am doing. Just faster than ever before.
But I'm for unprincipled optimism.
Math jobs are either in:
- teaching, which except for tertiary education, is poorly paid
- or a very limited, competitive and unstable pool of jobs in academia and maybe a handful of companies with large research departments
We're probably talking 50 000 people in math research worldwide and probably millions of underpaid regular math teachers at middle and high schools.
It's like engineers in post-Communist European countries, sure there were tons of graduates, but 80% of them were doing something else than the thing they graduated in.
Its kind of in Grant's incentives to push the interest for mathematics, because without an audience he won't be able to keep doing what he loves.
Like, my old uni has a history department, and had an Egyptian history teacher. This was at some point deemed a pointless use of resources because there was no role in society except for teacher of the same subject after that, and the classes shrunk, and she ended up getting offered a role in admin. She was not happy in that role.
I think it was relatively soon after that interaction that he started doing youtube full time. I've always wanted to think I made a teeny tiny contribution to move the needle there :)
- Grant is a highly respected and popular YouTuber. He has a strong network, personal connections, access, and his income comes from an audience, not from output he’s measured on. He's perfectly positioned in this AI revolution to end up near the top of whatever human pile gets constructed, so he will not have the kinds of fears and anxieties that most people do.
- AI RSI is being actively developed and is likely to arrive within 1-2 years. I wouldn't consider this a fringe scenario; it's the main bet. Even if models stay weaker at theory building than humans, organizations will spin up 100k agents and the fire-hose of generated ideas will probably compound far faster than anyone can keep up.
- His remaining arguments are basically training people to problem-solve, and joy. For the next few years, I can see his particular niche doing quite well as infotainment, and he will probably make a lot of money. However, I don't really see people being able to join and partake in his industry 10-20 years from now. Also, if we project a realistic and grounded understanding of our current world onto the next couple of decades, what would give anyone the idea that political and economic systems would have any incentive to train people to problem-solve if AI becomes the real work-horse? Teaching will likely be defunded and turned into a consumption good (which it arguably already is becoming with these YouTube channels.)
- So, for me his entire argument boils down to... joy?
Others have already commented that this feels like unprincipled optimism, and I agree. I also think that because this is something made to generate revenue through a social media platform, it's inherently performative and on-brand. His incentives pull toward keeping his audience happy.
Unfortunately, outcomes follow incentives, not optimism. If our economy comes to rely on RSI-enabled AI, most people will simply have no place in any industry it touches.
Then there will be no economy. If anything, if we reach this level of economic automation, more people will have to find ways to occupy themselves and sparking joy through math might be the best way to go about it for some.
But, if I get the insinuation, this would still require a huge social change to absorb once broad consumer demand falls off.
As for pursuing math for fun: that would turn most disciplines into something akin to speedrunning, chess, or mountaineering. People would add constraints to make it harder for themselves and compete against each other, and that does motivate some - but not all. A lot of people want to be "on the frontier." If discovery gets automated, the remaining frontier may be physical, actually going places no one has been, and that might pull those people toward space as it opens up.
> and other AI systems buying from each other
there is no difference between AI bro and a taliban, both methods of thinking are deranged, inhumane and show a grim future for the world at large
might as well as replace AI with god and you will understand what I mean
It can easily reorient itself (and arguably, already has) to serving the demand of a small minority of asset owners rather than the majority of people. E.g. people building luxury yachts and working to maintain them, working in luxury restaurants, maintaining luxury gardens etc. instead of working in roles that improve the lives of the majority.
Because most people are working on things that improve the lives of the asset-owning minority and not of the majority, the standard of living of the majority is not improved, they have to work more for less.
How many high-paying jobs today actually do anything that benefits the 'common man'?
First, "cognitive labor" is a form of labor - it's different vs. creative work, even though both use your mind. If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work. Cognitive labor is a form of labor. Let's talk about physical labor and leverage to understand how removing labor translates to time. On your farm you buy a tractor to replace your backhoe. If it is a hobby farm you get in the tractor and you're done super fast. Or, you can take that tractor, buy a bigger farm, and spend the same amount of time you'd have spent backhoeing, but in a far more leveraged way. You can trade removed labor for time in a way that suits you.
Second; the joyful moments we get from finding generalizable abstractions and nice solutions are an adaptation. Humans can climb infinitely high conceptual hierarchies - we'll never stop climbing, using the previous ones as tools to find the next. As we do, we gain joy with each discovery because. We get so much done with brains that run on 20 watts - are we tuned to receive a neurochemical reward for finding cognitive efficiency? If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
Third; everyone else is doing it, it's a baseline skill. Knowing how to work without AI is like knowing how to ride a horse. Useful and fun! Bedsides - only 150ish years ago horses were the only viable transport. Cars were new; toys for the rich. But cars got so good so fast that we eventually reconfigured whole cities. Your homework is to consider why and how horses got disrupted.
New divisions are emerging in the lump of roles humans had at work. AI takes away roles from your job and lets us do more with less. That's identical to every mechanization before it. It's killing some roles that make up your work, even as it creates new ones.
There's so much to be excited about. Fear is a rational response to change. But so is hope :)
Math is very similar, and requires an even higher degree of mental understanding to produce advancements. The effort spent trying to prove theorems and connect theories pays off in deep intuition; removing that struggle significantly impairs our understanding.
So no, you can't "be done with that, and go do other great work" without paying the understanding tax. And over time that's just not sustainable.
A simpler analogy would be gym training: the effort expenditure and the strength gains are inextricably linked. You can't go in there and start lifting weights with a forklift while expecting strength improvements.
In the case of software development, businesses have decided that speed gains are more important than maintainability, understanding, and independence. Will the same happen in math? The future in which mathematicians become LLM assistants (as opposed to LLM-assisted) and spend their days "turning the crank" just to review what comes out is quite bleak.
Doing weights is not the same as say, updating the gym with shiny new weights; or migrating all the weights in the gym to metric. At the gym, if the current weights need to go and new ones installed, a forklift will one-shot it.
Seeing the difference empowers you to choose the right approach for the right situation.
If your painting can be painted in partnership with an LLM, wow!
If your essay can be written in partnership with an LLM, wow!
If your painting portfolio website can be written in partnership with an LLM, wow!
If your museum show can be designed in partnership with an LLM, wow!
If the placards next to each of your paintings can be written in partnership with an LLM, wow!
If the car that takes me to the gallery can be designed and driven in partnership with an LLM, wow!
If the newspaper or novel that you read on the way to the gallery can be written in partnership with an LLM, wow!
If an LLM can give tours at the gallery and answer questions asked by visitors, wow!
If an LLM can write the music that I listen to on my way out of the gallery, wow!
If an LLM can synthetically perform the music, too, wow!
> If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
I don't understand how a person can say this with a straight face. There has been so much discussion of this, and so many reasons have been given, that one can only assume that, if you're asking the question and you have thought about the issue and read what people have said, you're not only asking rhetorically but have some personal reason for insisting on a frankly pretty frustrating, borderline insensitive insistence on being positive. I'm not trying to be snotty or rude. I just want to say that to me there is something uncanny about your comment, in its total blindness to any of the reasons someone might not only disagree with you but grieve the death of, say, their academic discipline in its current form -- and in its weirdly breezy lack of empathy.
Are you suggesting that if an AI could do all of those things to your satisfaction you would not be extremely impressed.
I do have empathy for people who see the world changing and are forced to adjust. That can be uncomfortable, but it is something that is inevitable with the changing world. It has always been this way, There is very little need to make swords these days, and as anything becomes superseded there are people that are attached to the old things and there are people dependent on the old things.
I think it entirely possible to have sympathy for their position while disagreeing that the solution is to prevent change.
I don't see this as a breezy lack of empathy. I see this as a hand reaching out and saying 'Hey, you can come this way and things aren't so bad after all'
I would not press it.
Yes, if LLMs can do all everything I listed, I'll be impressed. I'll also want nothing to do with any of it.
As I wrote in another comment, I want mathematicians -- in their current form, doing work as they traditionally have -- just as I want writers, philosophers, etc, because this is a better world that makes people better.
OpenAI's proofs do not make people better. They do not make our lives or work meaningful. Quite the contrary. OpenAI has clear-cut and salted fields that people have been painstakingly, lovingly sowing and cultivating for generations -- profoundly ugly actions that do real harm to some of the best of what people are and have produced.
If I were a person willing to hit that button and 'upgrade' my daughter, I don't know whether I'd be able to live with myself. I'd feel as though I'd killed her or at least done profound, unforgivable violence to her. She deserves the chance to grow into the best version of herself. What companies like OpenAI are doing is, if their plans pan out, at least as horrifying. It isn't progress. It isn't good for people.
We're not taking about attachment to old ways. We're talking about attachment to human value.
The journey is the destination. I don't care how many checkpoints you can breeze through, if you don't grow, have an experience that transforms you through the process of doing it. And if you're just ticking boxes by means of having a machine do it all for you, there was no need initiating the process in the first place.
I am not talking about producing tools that are means to an end here. I am glad we can make millions of socks a week by means of automation. But intellectual endeavors are different.
The point of doing math is not proving theorems. It's to discover the intuition, the underlying phenomena, internalizing them and adding to the human understanding of the problem. Writing out the proof is just the incidental outcome of that process.
If no human learns anything, if we just start producing testaments to a human null process where no person has emerged strengthened from it, we are no better off than we ever were. We are just producing empty and meaningless representations of something which is not there.
If so, what aspect of that makes it different? It is a change in the same beneficial direction. It is an intervention against what has happened naturally.
Similarly if she lacked any empathy and you could press a button to provide it? This would be the same direction of the same property, just an intervention from a different naturally occuring starting point.
I make no claim of the merits of OpenAI's immediate behaviour. I am commenting on a world in which things like this can be done, and like Grant Sanderson, I see a world of opportunity for understanding and learning for the joy of appreciating the problem and the solution. The only thing that seems to have been lost is that a human may no longer gain the prestige of being the first to discovers something. That should pale into insignificance to the benefits of understanding a thing. I'm not even sure if you should consider prestige as a healthy motivation to discover things.
Right now AI can provide a proof that is either valuable or not. If it is just the last page of a novel without any of the chapters then it hasn't given us mutch at all. The problem isn't in what it has provided, it tha't we've been using the wrong measure of merit.
If it does provide a full result with a rich explanation that people can understand then it has undoubtedly provided something that benefits the world. No human is awarded prestige for the discovery but that has always been an unfair measure.
If you work all your life on a math problem only to have an AI produce the result before you, how is this meaningfully different for your experience to working all your life on a math problem only to have another person produce the result before you.
If there is something that is unknown and could be proved true by path A and proved false by path B by definition nobody knows which path to follow. What happens if two mathematicians attempt this problem one going down each path. If an AI produces the result before they finish have they lost to the same degree? Only one of them had any chance of gaining the prestige. Did the other lose nothing? Was their life wasted? I don't think so either way and the only way to consider that work not wasted is to consider the effort to understand to be the thing that is valuable, not the result at the end.
If a solution is found by a human when there are people tying multiple paths, the one who guessed the correct path gains the prestige. That doesn't seem like a fair way to reward effort.
If we want understanding then AI can help.
Chess has had this moment. Computers can play chess better than people. It has also been a great benefit to the understanding of chess precisely because they value the how to get there over the result.
Prior to modern chess engines you could hypothesize about what the best move might be but you could never know if you were right. The fact that chess engines beat people so consistently is because often the guess is not right.
Chess engines gave us the ability to look at a game and see if if a player could have made a better move. They could then look to see why it was a better move. People then learned how to play better. They still play against other humans because they are testing each others understanding of the game, for that the computer is set aside.
Computers playing chess better than humans improved chess for humans.
Is there a compelling reason why that cannot be true for other things that they are better than.
Actually I think we need to go further, we need to make an example out of the people who spent a trillion dollars building a product that is universally hated to try and make a buck. They need to be completely ruined financially, now that would be a real challenge, I sympathize with those adversely affected but it needs to happen if society must progress to a better place where humans flourish more.
Steam engines aren't very good at designing steam engines. I think this time will be different.
Why do the labs have thousands of employees? Lets think about this...
Who's designing the evals needed to validate the model quality, who's deciding what goes in the system prompt? Who's negotiating to buy training data from hundreds or even thousands of data vendors? Who's responding when the Internet goes apeshit over some prompt tweak that makes models over-verbose? Who's out there listening to users and feeding what they say back into the product pipeline?
Computers????
However automated things get, that quickly becomes the new baseline. Customer expectations are always going up.
And as soon as humans figure out how to automate any of the things listed above - it becomes part of the new baseline too. It's always advancing. To beat the baseline and be competitive, you need humans. No matter what. No matter how automatic the automated things get. Always and forever. Because you need someone to drive, to find the next automatable thing and automate it - and to prioritize where to search for automatable things.
If we look at history of automation throughout the times it always decreased the amount of people needed to do the job. If you can't see a future where this new steam engine learns how to do a better steam engine, then you are blind. With the trajectory we're on it will happen sooner or later, and most people are having existential crises because the amount of humans required to be "in the loop" are decreasing increasingly fast.
Roles go away and fewer people are needed to do a thing, but I think it's good! For example the number of people on farms decreased orders of magnitude over the past say, century - yet we still feed everyone. Farming got mostly automated and got insanely more productive per human.
What happened was those people who would've been needed on farms went and did other stuff and the economy got way more complex but also that new complexity let a lot of more awesome things got provided for a lot more people by a lot more companies, a trend that continues today.
If you want to be a farmer good luck; it's harder to get started than it was say, 50 years ago - so why bother when there is no net new demand for farmers and there are also many better ways to make a living.
That's what'll happen for cognitively drudgerous work vs. creative new work.
No, it's not the same as mechanization. The fundamental difference, and why I find it illogical to argue either for "AI will open up tons of new work avenues" or "AI will kill all jobs" is that it all hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
If the former is true, then yes, there will be a lot for humans to do. If the latter is true, then no, there will be no reasonable cognitive role for humans to play (beyond perhaps for some legal, "nostalgic" reasons or what not). So whether one decides to be optimistic or pessimistic really depends on if you think AI will stay at a level below humans. I really don't know, so I'm not "taking sides" in this debate.
What would be the limiting factor?
For example, much has been recently discussed about how OpenAI's math results, as impressive as they are, remained within "the convex hull" of existing math literature. Thus, some have argued that the way LLMs work will keep them squarely within this convex hull, and also there seem to be clear examples from human history where humans came up with breakthroughs that were outside the convex hull of ideas that existed at that time.
There has been a lot of recent debate, both for and against, this idea that current AI approaches are limited to this convex hull. So I'm not going to try to convince you one way or the other, but I do think it is at least a plausible explanation of how/why current approaches end up hitting a wall.
I'll also show my bias which is to say I certainly hope they hit a wall, because I don't understand how anyone can think that humans won't be truly and completely fucked if AI ends up far surpassing human intelligence.
some proofs of famous conjectures (for example unique games conjecture) have been described as creating new, insane, almost alien ideas. Scott aaronson has a blog post on this.
I agree with you, just wondering your thought on how we will know the latter has come true? As I understand it, you're describing ASI, not AGI. The way I personally define AGI, we are already there.
On the other hand, if we are going to survive as a species for a long time it probably depends on us learning how to not be the most intelligent thing around.
Even if it leads to our demise, I don’t think willfully holding ourselves back is the way forward
What the fuck?
Sure, but you don't need very many people to do that relative to the billions of workers that currently exist.
If you wipe out 90% of all jobs instead of 100% the practical implications for society as a whole are roughly exactly the same.
The Great Depression was "only" 25% unemployment.
Humans keep a few around for entertainment but that’s about it.
The point is that people, like horses, can do other things. Humans don't even have to be better than robots at anything. It's the principle of comparative advantage.
I don't consider this a good precedent to the AI situation at all.
When this happened, humans went off and started doing what we now consider "knowledge work" (well, after a brief stint in factory work, where they also got displaced by automation). They escaped massive unemployment by being smarter than the tractors and mechanical looms. But how do they escape AI job loss when AI becomes smarter than the average human? or smarter than the smartest human?
In prior displacements humans moved up the stack. There is no longer room for them at higher levels of the stack if AI beats them at cognitive labor.
There's a better chance that a humanity-aligned AI would make sure that humans have something to do and keep us alive versus a capital-aligned one. At the same time, if AI would be the deathblow to capitalism, that'd be very, _very_ ironic.
That said, other humans can and will put AI to use in ways that don't benefit humanity. It's actually already happening - newsfeeds waste hours of people's lives and attention; give teens low self esteem etc etc. and guess what. Society is adjusting - governments via legislation, device makers via screen time limits, communities by spreading the word and raising awareness
Smart AI wielded by people without your best interests in mind may be tough to counter; but you don't have to do it alone: humanity is getting wise to the threat. We don't have great tools but it'd be against the grain of history to assume we won't come up with them in time. Can't give specifics - as they say, predictions are hard, especially about the future..
We've made it through bigger more violent upheavals and we'll make it through this.
And the guy is not a mathematician primarily - he's a Youtube creator and entrepreneur. I liked a lot of his videos but now I usually just ask the LLM for detailed explanation and I can probe it as much as I want if something is not clear enough.
Education will also take a huge hit, you can't really beat an almost free supergenius that has all the time in the world to explain something to you in as much detail as you wish.
It is not, and for the same reason it's not over for mathematics. For anyone doing anything truly novel, and yes there are still software engineers out there doing that, it's still inept.
It's de jour to leverage formal verification as LLMs are quite good at looping it, but that's still a tool we had to invent to solve problems. It'll be truly over when we're being outpaced in the realm of invention but I have seen absolutely nothing to suggest that has meaningfully occurred at all. Coding by hand is not gone, there's just less of a reason to do so now.
3Blue1Brown does an amazing job of making math interesting to learn in itself. As opposed to the hundreds of millions of kids told “You just have to learn it or you’ll be dumb. Keep up or you’ll fall behind forever. Go!”
The vid calls out explicitly that math education is a primarily a motivation problem and I agree. One way or another, we need a lot more focus on that.
When you have limited time to learn as a student, you either have the smarts to learn in the limited time or you cheat.
I can't help but feel how this is all industry-planted, and I wouldn't argue its too far fetched.
It seemed riveting enough for some mayor mathematicians to "decode" his solutions into readable proofs?
The only difference I spot now is that it was not an Indian man, but a machine. If that bothers you still, it seems less about the art of the craft being taken as it seems to be about who has taken it?
Reflecting on that a year later is interesting. Agents have become REALLY good since then, and I consider the "writing code" side of my profession to be largely annihilated. Some days that's really hard to accept.
But I think Grant's conclusion about math still largely echoes what I wrote about software: don't underestimate the social aspect of these activities, and if anything AI has made the social side more important. I deliberately avoided declaring, "now is the best time to learn to write code". I suspected that skill might be going out the window. But learning systems thinking and the social skills needed to connect people's dreams to reality continues to be an important art, an art I still have the privilege to practice every day.
And if we do reach the "anything you can do I can do better" stage, then, as Grant said, that's a hard to imagine world, and one where "it can write really good code" might be the least of our problems.
You also aren't going to get an accountant running 4 simultaneous streams of AI-driven development and working through an AWS issue when something goes wrong.
No comment as to the next generation of AIs.
Second, if "all software vendors in all spaces get wiped out" was going to happen I think we'd be seeing more of it already. Yes, there is support for some software vendors possibly getting wiped out... but, then again, you can't look at a bad vibe coded implementation of "the entire Adobe suite" that was rather overblown in the press coverage and forget that Adobe also has AIs. Instead what I'm seeing at my own workplace as we ponder the question of "should we replace this service we buy with some local vibe coding" is still remaining but we don't want to support that. Can we replace Confluence with vibe coding? Yes, but that was true five years ago too and we didn't want to do it then, either. We still don't want to do it. HN commenters have always overestimated the desire everyone in the world has to become programmers and take responsibility for everything.
One wonders what percentage of those who are certain that vibe coding is going to nuke all software vendors can't even be arsed to self-host a Jellyfin or VaultWarden install... which is way easier than vibe coding the whole of those things from scratch, and we're talking about people who are already programmers. Physician, heal thyself.
But no one has nailed that paradigm yet.
I think social skills are much more important today because one person can do so much more but this person needs to talk to many others to know what to build.
I will miss coding, but I had a good run. Time to learn a trade. I don't begrudge this fate.
If AI solves all coding and software then we are not going to sit around talking, it will be the time to sit down and do some very complex deep work that needs silence, concentration and understanding.
For you it will be paradise, you can also just point all the people to talk with your agent instead of you.
I liked the coding part.
> If AI solves all coding and software then we are not going to sit around talking
> it will be the time to sit down and do some very complex deep work that needs silence, concentration and understanding.
Have you worked at a big tech company?
But if, somehow, you can find the right thing to build without talking to people, there is still a lot of building to do.
Good luck, I think we are all going to need it.
And a lot of that building is of tangible things in the physical world, that I can literally feel the good of.
When everything you ask for is instant and valueless, even asking becomes meaningless, and everyone is waiting to see something they'd not thought of.
Then, a thousand thousand copies, immediately… but also, watching that person like a hawk to see if they can do it again. That's the future. A lot of people will just plain become unable to think or intend anything on their own, or even want anything.
Somebody still needs to determine what the company system actually look like, that someone is still probably a programmer, it doesn't matter anymore if that programmer is also a good coder.
Edit: and yeah, even teachers probably have lots of chores and boring parts of the job.
This is already happening in CS and math.
Only if the goal of a pet project was the end result. In my experience pet project is all about learning new things and exploring the unknowns. LLM finishing it in half and hour does not achieve any of that. Although it can be a good assistant.
On the other hand, you can set up an LLM so that everything goes gradually and you learn like you used to. But that's more like what I would call pet archaeology or something... Learning the tools doesn't give as much benefit anymore, it's more like a reconstruction of past events.
Like calling Lee Sedol a pretentious tool for retiring in the face of AlphaGo. If you really do mathematics for the enjoyment of doing mathematics, following a roughly unbroken line of tradition for at least a couple hundred years, an alien computer mind showing up and smashing everything would perhaps be upsetting, don't you think?
Nothing is stopping anyone from thinking deeply about math. The angst here is about whether they can get paid for it or not.
Then I finally realized that Professors spend most of their days in meetings and management - not actual research!
Mostly Funding. Then each other. Then the myriad trivial yet bureaucratic things of daily life. Then research. I'd put research at like 10% of a week, so maybe 5 hours total.
Frankly, despite the obvious financial worries, it's been a little freeing. I can go do something else (because, uh, I may have to).
There's never been a better time to be a professional mathematician, perhaps. Just like there's never been a better time to be a senior software engineer.
An 18 year old entering university today will retire somewhere in the 2070s. Is mathematics, or software engineering, a promising career path for the next 50 years? No, it's most certainly not, and anyone suggesting otherwise is delusional. I don't know what would be a good career path, but most certainly avoid anything that AI is having the most success at in 2026.
It's fine to follow your dream, but just make sure that your dream wants you too.
It also helps to have rich parents, if you grow up poor you understand the consequences of choosing the wrong career path can be devastating. Some people have the freedom to experiment and still get a soft landing, other people need to get it right the first time.
If AI came about 40 years ago, it would have been much more restricted and advanced much much slower.
But politics does not care for the average worker anymore. Every democratic country is slowly turning geriatric, so due to how democracy works, the will of the OLD is what runs societies. And job security is not one of those things, when the biggest voting block does not even work.
People who want to solve problems themselves should go on to invent them without posting them on the internet until they're solved.
Yes, cue the: cope seethe, selfish mathematicians, care only about personal glory, more theorems = cancer proven, more knowledge>less knowledge, e/acc etc. etc.
I've heard all these tired arguments many times. Whatever - I concede - you're right and I'm morally wrong and bad. Just don't expect people to study this subject which is basically being turned into biology (spend hours sitting in a lab babysitting equipment all day while watching a movie - it's what most bio phd students i'm around seem to do, no offense meant to bio phd students, i'm certain their studies are orders of magnitude more impactful to the society than mine).
it was fun while it lasted.
There's a number of them that absolutely loathe it.
Your point about biology does not sound fair, an ex of mine worked in the field and that is not at all what she did.
My view is that the people who think doing maths is about being able to knit maths quickly and correctly are quite sad.
But for the people like me who bound themselves to computers a long time ago, it feels like a revolution. Sure you might now be simply tending your garden of machines and allocating capital and resources like a Gardiner picks seeds for various sunny spots but you can now do a lot of stuff and for people were good at gardening but not knitting it is a game changer.
I saw some clearly AI slop made videos and got much better understanding of topics, since they don't do foreshadowing for an awe-inspiring connection that we'd admire together after 15 min videos, the clankers just get to the point. Not claiming those videos are too useful either, but I did however see accelerated learning gains from asking LLMs to explain (and do Bret Victor-style small interactive demos) math and algos, something I have never experienced from any of the educational STEM Youtube channels.
As for "fresh learners", I can provide my own son, who watched the series before taking his first linear algebra class, and says that it helped him a lot.
Uh huh, and what if the videos make me more generally interested in the topic? How would you measure that on a test?
Your view seems needlessly pessimistic and myopic. Just because something might not increase a number on a test that doesn't make it pointless.
EDIT: And don't get me wrong, I hope it doesn't happen for a long time, ideally never. But what would his arguments be if it does?
"There's never been a better time to go into math" was the final statement of the ten minute orientation session from the Dep Chairman.
It was a great thing to do anyway.
Then.
There ought to be people watching his channel who wonder whether given all these AI advances math is even worth studying now.
get the peer review engine going
I imagine its happening but I also see room for coordination because I don’t hear about it happening, and its only been a few weeks
I don’t trust that academics will pivot in a few weeks and I don’t trust that this peer review is occurring on a big enough scale
Where could I go to understand whether something useful is coming from these AI proofs
Everything I’ve heard so far is debating about how the proofs came out and what academics are supposed to do with their lives now
I and many others want to see what utility these probably solved problems give us
Someone once described a mathematician as a machine to turn coffee into theorems. Okay, fair enough, but what sets mathematicians apart is that mathematics wasn't a choice.
It's possible that Sanderson doesn't get this, but people watching his video either will never understand his argument, or have always understood it.
Instead, people who sell shovels win big.
The number of pie eaters (equivalent to workers) got bigger.
My answer to your job is that more jobs move from secondary to tertiary sector (entertainment). That has happened usually.
In a way ai is turning programming more into maths - you write a natural language description of the problem - a proof / program - and then translating that into machine code is a lot of work / abstraction. For example look how much it takes to turn relatively simple mathematical statements into lean. That I guess is going to be the future.
I would encourage everyone to learn the fundamentals still because you will need discretion and to be able to think at a more abstract level.
However its funny that its only NOW dehumanising/demoralising now when its white people losing jobs to the capitalist machine in the imperial core, and not the slave silicon miners making gpus for gamers.
Machines have been doing arithmetic (add/subtract/multiply/divide) better and faster than humans for 70+ years. I would ask anyone making this claim, "are you OK if your children do not learn basic arithmetic?"
That said, you'd be missing a bunch of hand-made illustrations and animations from one of the best math communicators in the world. If that's not appealing to you, I'm not sure the transcript will do much for you either.
It is make like better. You're just invested in ripping out others' tools for your own satisfaction.
> Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well.
The difference between this & the backdrop of Dune is near 0, with its issues clearly outlined in the book: You want the system that existed in the 2010s to remain as-is & ossified for your personal enjoyment.
A lot of arguments seem to try to cling to the “old” way of doing math: staring at the blackboard for hours, wrestling with papers and papers of equations, and do forth. Well, chess players went through a similar transition period: carrying books of openings and such, to chess database, to chess engine and now AI. And at no point I hear chess players complaining that we have to study chess the old way.
This is very much discussed in the video.