A misalignment of AI in mathematics
mathandai.org696 points by meredydd 9 hours ago
696 points by meredydd 9 hours ago
https://terrytao.wordpress.com/2026/09/11/a-severe-misalignm...
https://www.economist.com/science-and-technology/2026/09/11/..., https://unwall.app/www.economist.com/science-and-technology/...
As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skepticism, but it also generated conferences, papers, talks in the hallway, discussions with students, and so on--a flurry of exactly that kind of community process that the declaration says is the main driver of mathematics. Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc). Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. It’s frustrating that this comment is at the top because it absolutely misrepresents the actual declaration. The declaration is absolutely not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what some of the current problems are. The maths community is now in the antithesis phase, synthesis will take a while ;) Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available. But on the other hand, people learned a lot from chess engines. After decades of chess computers beating humans, there was still a renewed interest in watching Leela beat Stockfish, with many people trying to understand the strategy Leela used. If your happiness comes from grinding on a problem and making progress, the prospect of having to dig through a corpus of AI-generated proofs might be hard to swallow. But if you're willing to do that, you will still find beautiful things that only so many people can truly appreciate. Chess is kept afloat by a couple of billionaires like Sinquefield, MBS and the guy who sponsors freestyle (Fisher random) chess. Carlsen is bored by studying engine lines. The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content. I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now. Chess is kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on. I think the parent comment meant professional, high-level chess. The kind people get played to play, not just do for a hobby. That's absolutely on life support. I'm not sure what the equivalent would look like in the math field, but it probably involves a lot of mathematicians losing their jobs and the quality of human-produced math decreasing overall. The quality of the math in general would be fine, since in this scenario cpus will keep producing it. The quality of cpu-cpu chess games is quite high, beyond human understanding in many cases. Chess is a weird example because it doesn't really have any utility beyond itself. Even pure math sometimes ends up having use in the strangest places. Although if no one understands the frontier math (because no one is getting paid to), I'm not sure it even matters what the quality of the cpu math is? It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? "Although if no one understands the frontier math (because no one is getting paid to), I'm not sure it even matters what the quality of the cpu math is?" Presumably AI will be connect the dots to the applications. As the declaration says, this isn't just about math. Human understanding is losing economic value. You can understand stuff on your own time, I guess. The standard justification for pure math to holders of purse-strings is something like "it might lead to a useful application down the road, like crypto, who knows". That looks pretty inefficient now. We have to entertain the possibility that AI can develop the math needed for any application we put to it. Eg if number theory didn't exist, we could have asked AI for a way to transit messages securely and it would maybe come up with fermats little theorem as part of its solution or maybe come up with an approach we can't conceive of right now seeing as most of us are constrained to available number theory. Like how in the last year when I give an LLM a programming project I see it doesnt even bother with of the many software libraries I and others have written and just codes up the calls it needs on the fly or finds some other ad hoc solution. I would argue people getting paid to play chess was a short lived phenomenon anyway if you put it in context. The transition there is less related to the introduction of chess engines and more related to the shift in the media landscape. Mathematics is more than establishing arbitrary facts (although some look like curiosities), it's also defining what interesting research directions are and establishing common language/notation. I think that will stay relevant? Why? How do you define interesting research directions? That used to be defined by testing the limits of human understanding i.e. some people can't figure something out. AI might have very different ideas about what is interesting and I am not sure what humans would get out of putting years into understanding AI proofs for what? What are we doing at that point? Like if you spend years understanding some AI proof of theorem 123456, why is that meaningful? I am actually asking why you think defining interesting research directions will stay relevant. In my opinion, people spend years acquiring knowledge so they can work on problems which is separate. There's two points about this I am assuming 1) Mathematics actually has a significant subjectivity to it and is community oriented and not just climbing a never ending list of theorems that exists in the universe 2) A lot of mathematical research work is inside of a subfield and isn't directly motivated by applications. Sometimes it is but e.g. people don't work on obscure theorems about elliptic curves because of a dire need for that but more because the community found it interesting. In theory you can automate finding interesting research directions by identifying conjectures with many dependencies. And notation has never been mathematicians' forte, with them trying to cram the entirety of universe into single letters. People become interested in things when they become invested in it personally, because they've contributed to it. So I don't think it will stay relevant... > It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding them. > But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. What is the purpose of that? Its like art being produced for AI to consume. What is gained from that? It's going to be hard to compete with something that has access to all of math at once and can find connections between elements that appear unrelated to humans. And at some point AI will start suggesting - or doing - physical experiments. Well if it proves useless presumably they'd stop doing it. But if AI is to recursively self improve understanding and evolving its own foundations, which are clearly mathematical, is essential. There is no need for humans to grasp what is going on in that loop. I mean, was the point of math ever just because some humans enjoyed doing it? Even though a lot of it is theoretical, there's been all sorts of useful things that have come out of it as well due to an improved understanding of the universe through new ways of thinking about it. If it got to the point where no human could understand it and there were no ways to actually use it, I don't think anyone would bother having their computers doing it at all. > was the point of math ever just because some humans enjoyed doing it? Yes. Friends and I often work on Putnam problems and this series: The (Almost) Impossible Integrals, Sums, and Series by Cornel Ioan Vălean wouldn't AI solving problems in science, engineering, economics, etc be able to apply the new AI math? >but no one understands it, did it make a sound? Does your "one" only contain humans or does it also contain other AI systems. AI math is not a single monolithic thing, but a distributed one. I see value in sharing proofs even among just AI. Also, you learn to be a better chess player by... playing better players. The widespread availability of chess engines has made flawless opponents available to every player. If your goals are understanding the game, self improvement, building thinking skills-- this is the best chess has ever been. It's only if your goal is to beat every opponent you can find that chess is in a bad place. It's not that easy. Playing stockfish is like playing tennis against the wall (for untitled players at least). Even if you don't blunder anything, you'll still find yourself in a worse position without any clue as of what went wrong and why. Whereas when playing humans, they can usually explain their approach and when they noticed errors in your play. I mean, I'm not a great player but I've learned a lot from working through games with stockfish using a git repo and a small script that lets me rewind to different moves and try different approaches. It may not explain its moves but if you're thinking through what's happened you can usually debug your game anyway. > Playing stockfish is like playing tennis against the wall (for untitled players at least). It's the same for Magnus Carlsen. Even with Queen odds, Stockfish is literally unbeatable for the best players in the world. It's just too strong at evaluating all kinds of random tangent moves (and ensuing positional advantage) which no human player can possibly pay attention due to the time required. Stockfish vs any human is like Carlsen vs other players by about 3-5 orders of magnitude[0]. It's that stark. [0] A wild pun appears. EDIT: To avoid having to respond to each responder, fair comments about Queen odds. Maybe I was thinking Rook odds? Also, I kinda lumped Stockfish in with all the other engines, but I realize there are other engines with different properties ofc. Well, that's actually not true at all. Stockfish is not a very good odds player and at queen odds is easily beatable even by bad players like me. It will just trade down into more trivial and easier to win positions that it perceives as "less bad", since everything is super-losing anyway when you start down a queen. Leela odds networks, on the other hand, are an entirely different beast. I cannot beat Leela queen odds, much less rook or minor piece odds, and even GMs struggle against Leela knight odds. Without odds though, yeah, Stockfish is just incomprehensibly strong by human standards. All top chess engines are, but Stockfish moreso. No worries, I know stockfish is unbeatable by humans. But sometimes, these GMs can flag it, which counts as a win (especially when it's proxied by a cheater). Sometimes they can also explain the idea that cost them the game, so they've learned something maybe. Whereas us scrubs literally cannot do anything at all for reasons completely beyond our understanding. > Whereas us scrubs literally cannot do anything at all for reasons completely beyond our understanding Computer moves are typically much more concrete than human moves: a human will play based on pattern matching ("intuition") and can only make explicit calculation of a small fraction of possibilities, after which decisions are guided by guesswork. The computers are unbeatable in practice because they can calculate concretely in seconds what might take an expert human long intensive study to notice, and they don't make the same kinds of oversights humans can make. But if you stop and explore a particular position for an extended time, and if you have an intermediate level of chess skill, you too can probably often (usually?) figure out why it's doing something. Sometimes understanding the computer's reasons takes searching multiple branches of a tree several unlikely looking moves deep, but the collection of threats the computer was preemptively thwarting, traps it was setting, etc. are comprehensible to humans with enough effort, especially in games between the computer and a human. The frustrating thing about playing against the computer is that it notices and thwarts every plan you might come up with, before you make up the plan yourself, and it doesn't make (human-apparent) mistakes, so the game ends up feeling hopeless. Nothing you try works on it, and if your idea is even slightly inaccurate it will be exploited. I mean, this is the problem with analogies and trying to use them to prove things, right? People working through problems from an analysis book with their friend (or an LLM) is not the same as research mathematics. People playing in a chess club is not the same as what makes for a good chess tournament. Lumping everything together is just making this branch of the conversation less relevant. Chess is a fun game. That's why it's been around for 1000+ years. There was a renaissance during Covid and due to 'The Queen's Gambit' where it gained much more mainstream popularity, but... Chess AI was already far far (like 1000+ Elo) ahead of human players at that point. The thing is... chess is humans playing (communicating) with humans and that's what keeps it interesting. Check out the view counts of chess AI tourneys vs. human tourneys. I really hate this overly condescending takes. First of all, what do you know about the internals of math research that allows you to speak with so much confidence. Second, you're not even addressing the issues raised by the letter! This is not about "oh they made a bunch of problems easier". There are huge economical interest behind: who owns and has access to models? are these companies interested in developing research or they just grind PR stunts without worrying about externalities in how research is actually conducted? Etc etc. If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment. There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable. It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they don't think on the externalities. Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be. Tech companies are as much the topic of this post as AI, I think that's the immediacy. To a significant extent, the pursuit of mathematics research is a pursuit of human understanding of mathematics, without knowing where it might lead, or whether it might lead anywhere at all. I don't see how the motivation for that goes away on its own, but the institution supporting it is certainly threatened by the potential loss of grant money and graduate student applications. > No one is interested in watching two machines compete I’ve watched quite a lot of YouTube videos where two machines compete, so you may not be completely right here Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish. Stockfish does not steal research or scoop researchers. The concentration of computing resources and capital should be examined by the math community. This is the real problem. We're looking at a future where those who control AI have an insurmountable advantage in everything. They can control the amount of intelligence the masses have access to -- for their own safety, of course -- and they will never, ever be able to close the gap. Say they do. What then? Will people buy from them? What if we decide not to? Is this the scenario described in Ted Chiang's short story https://en.wikipedia.org/wiki/The_Evolution_of_Human_Science where scientists are "catching crumbs from the table" trying to decipher the results generated by superhuman intelligence? It's still an optimistic scenario. Artificial superintelligence may develop hypermathematics of a kind that never will be accesible to human mind, enhanced or not. One can't teach geometry to ants even if you put them on a Moebius strip. It would be more like Lem's novel where it completely disappears from the human horizon: https://en.wikipedia.org/wiki/Golem_XIV Which is why if humanity had empathy, it would be working on how to make smarter ants, so that they can learn more advanced geometry. I love that as a goal! Perhaps indeed a better understanding of what intelligence really is would allow this sort of Uplift (as in Brin's books). It's quite possible ants understand a geometry more advanced than our own. Ant Intelligence will be next big thing in machine learning after this bubble bursts What’s optimistic or non-optimistic specifically about the machine having a system of mathematics beyond our comprehension within it? Why should we care about that in itself? In the first case, we'd still have a chance to take a glance at the frontier of discovery (even if ordinary human mathematicians had to spent years translating what metahumans achieved). In the second case all human-level maths would be solved and what lies beyond would be always out of our scope. > Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc). This also sounds like a vector for trolling the community with complex putative proofs hiding a known flaw. Not if it's lean-verified. "Lean-verified" is not some magical incantation that makes a supposed proof irrefutable. Even disregarding potential bugs in the kernel as others have said. Say that AI gives you a Lean proof and says it proves Theorem X. It could just as easily give you the same proof but claim that it proves (not X). How would you know the difference? Nothing can really be considered proven unless a human expert can read the Lean proof and determine that (X as defined in the Lean proof) corresponds to X. The proof (at least the statement of the theorem) must be intelligible to humans to have value. It's possible people will just start taking AI at its word. Maybe AI says "Here is a Lean proof of X" and we all just shrug and go "Okay, X is proven." But that's not how it works right now for human mathematicians. Why would we apply that standard for AI? Didn't some of the recent proofs exploited a couple of blind spots of lean, and they were invalidated? Edit: Yup. A bug report to Lean was disguised as a "Collatz" proof in a humorous way. Links below. There was a hash collision bug in the main Lean kernel that was patched, but AFAIK nothing relied on it. You'd have to know what you were doing to accidentally get there... The incident in the links I posted exploited several bugs AFAICS, so it's a different story than a single hash collision bug, it seems. I don't know ... do you have a reference? >Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI. Title: Terence Tao - SAIR Competitions and the Future of Experimental Mathematics https://www.youtube.com/watch?v=rB9YOi3lb7w and this: Daniel Litt - Working with LLMs to do high quality math So he got exuberant because he is funded by SAIR and the "AI for math" fund. And embarrassingly they used him for a "coal miners should learn math" moment that just benefits the AI industry. He has severely reversed course in the past week. Without concrete propositions it remains to be seen how much of the new resistance is for show. I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have. AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanced math training because my experience so far tells me I will do well. How could you possibly know if it has potential or not? Sounds like AI psychosis setting in. Because every test I run with it is telling me so? The great thing about math is it can be externally validated. > Dr. Tao said the same thing. Apparently he has since changed his mind. Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance. Where is the difference? He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things. He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code. > He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing. The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead. Isn’t it more like it merges the code without a dev reviewing or understanding it? Pretty close, but IMO not quite. A math proof in and of itself is useless unless either: Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true. No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything. taste "I believe I did, Bob" lives rent free, every time someone tells another person to fuck themselves using technology. Thank You! Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise? But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. I don't like nuance here. I think progress is really measured by what humans are able to do and understand, not machines. It is significant if we find problems we struggle to solve. That tells us something. What does it take for humans to solve these problems is related. The best analogy I can give is if you wanted to climb Mt. Everest you might ask someone for guidance. Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak? This is like the AI versus human gap to me. The helicopter is like using AI to generate a proof. The person who actually climbed Mt. Everest has firsthand knowledge of the experience. Same thing for a difficult proof. The struggle people have is actually valuable here. Likewise, we know people are actually capable of climbing Mt. Everest but if they had only ever rode a helicopter to the top, the knowledge of climbing it would not exist, and surely that is meaningful knowledge given the risks. So if we rely on AI for proofs I think we lose a sense of what is difficult and why. We lose a sense of what human achievement is. Surely climbing Mt. Everest means more than taking a helicopter up? For students, why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? This would have the affect of destroying knowledge. (please do not nitpick the analogy because it's the best but perhaps a clumsy way to describe my thoughts) Tangent: > From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. Keep in mind those ~88 hours were spread across ~10,000 simultaneous agent instances. So, roughly 880,000 hours of compute. Assuming a fifty-year career, and forty-hour workweeks, a human mathematician's career is about 100,000 hours of "compute". I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already. The perverse incentives of academia mean this has never occurred. The perverse incentives of industry mean OpenAI intentionally scooped researchers who were getting close (granted, with AI help). I'm not trying to dismiss the achievement - if the proof turns out to be solid, it's quite impressive (though much less so if the training data included the recent human breakthrough, which seems pretty plausible). I'm just pointing out that "88 hours" is a very misleading way of framing this. ok I realize this is a tangent but you're saying my post is very misleading and then also saying that a human mathematician's career is about 100,000 hours of compute and that Navier-Stokes could've had a solution by now if not for perverse incentives. You may be right but I don't think this is a great argument because in a year I would bet that those numbers change since computing power tends to increase or get cheaper over time. So I am taking the stance AI can outdo people if not now, perhaps soon. > I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already. > The perverse incentives of academia mean this has never occurred. This. Mathematicians in their most energetic years are trying to get tenure or land a tenure-track job. They are disincentivized to go all-in on ultra high risk, high-reward problems. The potential downside is just too forbidding. It's much safer to develop a research program in a mainstream field that affords many opportunities for partial progress that can translate to a robust publication record. > Would it be better to ask someone who has climbed Mt. Everest or someone who took a helicopter ride up near the top and then went to the peak? Depends on if I want to go by helicopter myself. I agree entirely with what you're saying, right up until your final question: > why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now? I think you answered this yourself earlier: > I think progress is really measured by what humans are able to do and understand People want to make this progress. Therefore people will "grind Everest" as a mathematical community, and that is maybe not so hugely different from a lot of previous mathematical work. There's still ample room for creativity: simplifying, generalizing, asking new questions humans are interested in, ... That grind is emotional. And it's something AI will never have. The desire to solve a problem. Citation needed. Who are you to say large enough clusters of neurons can't develo emotions? I think progress is really measured by what humans are able to do and understand, not machines. Building a machine that solves Millennium problems is pretty cool too. You wouldn't know it from reading these stories, though. > Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc. I think a better comparison is: mathematics just becomes like mining bitcoins. I think you might have to explain that comparison a bit more to be honest. How are math proofs like bitcoins? A bitcoin has a pre-defined value, a math conjecture / proof is a bit more complicated. A Bitcoin does not have any pre-defined value. The value of Bitcoin keeps fluctuating, and historically has risen dramatically from its initial value of 0. If this weren't the case, there would be no investment/speculation in Bitcoin because there would be no potential for any ROI. In reality, the value of Bitcoin is determined by humans (even if indirectly, not by planning), and I think the OP’s point may have been that maths proofs can be regarded similarly. No intrinsic value, just what humans find in it. If there's a machine that automatically turns electricity into proofs then mathematics becomes a different thing altogether. The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem. > closing research directions left and right Why would research be closed in one direction? Even if AI or human says "Tried that, didn't work" or whatever, someone (or something I suppose) might very well retry it in the future, if nothing else to reproduce it didn't work, in theory at least. AI tends to take nearly finished research directions and push it to the conclusion in one step. If deployed massively, it will pluck all the low hanging fruits causing a drought of near term promising research project. Because people who start promising research directions do not get to see it finish, over the long term fewer people will start new directions, causing the field to slowly whither. Mochizuki's claimed proof of the abc conjecture was extremely unusual for the reason that nobody was able to extract a single useful idea from the argument. I was starting grad school when it came out, and my immediate visceral response was "if this is what number theory is going to look like in the future, then I will leave mathematics." The current wave of AI slop mathematics might end up driving the next generation of mathematicians away from the subject for the same reason that Mochizuki would have convinced me to quit if his proof had been accepted by the community. Luckily, my professors had the taste to immediately recognize that it was garbage. So it wasted everyone's time, thousands of hours of research trying to disprove something said very loudly. What OpenAI is doing is a DoS of the scientific community: wasting your time trying to check if they're not wrong, and claiming glory in the mean time. That's true, but the story would have unfolded differently if Mochizuki had a lean-verified proof and was correct. I guess baked into my premise is that AI is producing reliable proofs (in the long term at least). Agreed! Although, if done by a mathematician, it's not a ~complete waste. I think the community learns something along the way. Is there an established term for the idea of "DoS"? I've taken to calling it slop fatigue. Denial of service is the established term. Hammering their API (reviewer committees) would be an informal one Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity is growing while our human ability is stagnant. meta-AI analysis cannot help. We (software professionals who use AI regularly) already know that if you run into a situation where a Fable/Astra-generated analysis reaches the limits of our comprehension/complexity due to their subjectivity, throwing more AI at the problem doesn't always converge. There are many reasons to feel optimistic about AI, and ultimately its general ability to help science and mathematics. I see no reason to feel optimistic about the future of mathematics and AI based on the current path of frontier labs, unless the misalignment Tao is writing about can be reconciled. > AI is now capable of constructions so complex that no human or human team can unpack. How can we possibly know this when we haven't even seriously started on the endeavor of actively reverse engineering these AI-generated proofs? That's a proper job for human mathematicians, because the AIs themselves are demonstrably clueless about what steps in a proof are genuinely interesting and load-bearing from a human POV. This is evidence of a limitation in AIs' capabilities, not of any kind of misaligned behavior. The fact that Tao actually uses that term in his complaint is deeply disappointing. Not to mention, there are already (pre AI) machine-generated proofs that we've pretty much agreed not to try to explain fully, like the four-color theorem which ends up with brute-force verification of 600+ cases (down from close to 2,000 when first demonstrated) > there are already (pre AI) machine-generated proofs that we've pretty much agreed not to try to explain fully, like the four-color theorem Algorithmic verification is a very unsatisfying answer to the problem (e.g., surely it's not just dumb luck that every single case happen to have this exact property), but that's an entirely different issue than saying that no one follows logic of the proof method itself. For the interested; the saying I believe you are referencing in regards to writing code / debugging is from Brian Kernighan, specifically: It's prescient. It’s a cute statement, but it doesn’t really match reality. Programs written by humans can generally be debugged by humans. Could AI write programs that humans can’t understand or debug? Probably, but that’s not what Kernighan was describing. > AI is now capable of constructions so complex that no human or human team can unpack Can you give an example of this? The first major computer-assisted proof, of the four-color map theorem in 1976, was an example of this. It created a lot of controversy at the time. It used proof by exhaustion, i.e. essentially analyzing every possible relevant case, something that no human could do without the assistance of, at the time, a supercomputer. It's not just the isolated dumping, it's the fast, isolated, possibly untraceable dumping, without long term support. It'll basically become slop fatigue if OpenAI starts dumping out proofs faster than the community can keep up, and some turn out to be wrong, never formalize it, don't stay to support it, etc. I wonder if they will continue to dump proofs, though? Their point has been made, the novelty will wear off, and it maybe won't be a priority use of their resources to spend however many millions on another big proof--they will move on to the next thing to show off I'm sure. At that point, the ones generating proofs will be, I hope, mathematicians (professional and otherwise) that are more interested in the results and community discussion. (Well that's my hopeful, optimistic take, anyway.) They aren't going to stop at one, that's for sure. They already claimed they have "made substantial progress" on another millenium problem. Let's say they bag another one (Hodge and/or BSD according to the rumors), if it looks like their internal model could solve P/NP or Riemann Hypothesis, you think they wouldn't take that chance ? They already told the NYT that they’ve made “substantial progress” on another one of the MP Problems (most likely the Hodge Conjecture). That said, that’s probably just because of the drama miring their most recent one. After 2 I don’t see why they’d bother anymore. >That said, that’s probably just because of the drama miring their most recent one. After 2 I don’t see why they’d bother anymore. P/NP and the Riemann Hypothesis are part of the milllenium problems. They will 100% keep trying to crack those regardless. I think AI companies making a point is not the only thing at play. Discovering new maths ultimately leads to new technologies and applications. It may start theoretically but end up being of practical use in the future. Even if humans do not understand it (lose interest, too complex, or just way too many new proofs to go though) AI can use this AI derived math corpus which will help it in other fields. I really like this take, and while I hate math I value it. Your position sounds extremely plausible and it fits with the pattern we see in the community here.
Regardless if it's ai slop or not we still debate the value and attempt to understand. In the process generating new insights and ideas. Life will go on. I get excited at the idea of a world in which advanced mathematical problems (and their solutions) become much more accessible to a much greater number of people. As a result, making mathematics much more loved at a societal level. Imagine a world where these most complex mathematical problems are not accessible to a few hundred people, but a few hundred thousands people.
...Those original few hundred gifted mathematicians would have an even more prominent role, and their names and achievements would be known by orders of magnitude more people that they are now. This is the hope, but I suspect the reality is that we see an ever widening gap between the fortunate and the unfortunate. We're looking at the automation and commodification of all knowledge, and the best models will be kept locked behind closed doors so that they can't be stolen. And, of course, "for our own protection". As a laymen, I wish the same. But I also hope it doesn’t disincentivize those that dedicated themselves to the study Math department administrators fire Terence Tao. Based on current reward models, the frontier AI labs will burn down mathematics as an impressive display of capabilities and in doing so, will make it impossible for people that get paid to do mathematics to stay employed. If your job is literally to publish papers, and OpenAI and Anthropic decide that making an infinite-paper-printing machine is the best thing to show how effective their tech is, then as a demo, they destroy that industry. I wouldn't expect them to destroy that industry, imagine global squadrons of academics and mathematicians focusing their attention on LLM's, training algorithms, scaling laws, ... they're gonna try and beat the incumbent frontier AI labs, eye for an eye, tooth for a tooth The apocalypse being triggered by frontier labs picking a fight with mathematicians was unexpected. I've met a few Ph.D Mathematicians in Academia socially. My unfortunate experience was that they were insufferable,borderline hostile people. I tried to genuinely engage with them too. I've met one Ph.D Mathematician that left the industry whom was very enjoyable to talk to. I have a feeling that my experience was not unique and the Math world is mostly a bunch of too good for everyone on their high horse a-holes that are now being knocked down a peg. They don't like it obviously. I'm not a fan of knocking down things that work, however I also find it hard to be against death of the gatekeeping old guard of any industry. I think math is just gonna have to suck it up like every other industry now. Math productivity is longer out of reach of the average grad student. Like every other industry they are no longer untouchable and are gonna have to adjust to the new way of things or market forces will do what they always do which is refuse to fund ineffectiveness. I've had to accept that tech/IT will never be the same. Just how it is. You can thrash against it all you want. The rise of AI is going to lead to a lot of similar issues in many fields as it grows and develops further. This can be seen form 2 perspectives. The death of intelligence as we no longer need to think for ourselves or understand anything since AI can do it. Alternatively, and this is what I choose to believe, it will lead to further intellectual enlightenment and advancement for use as a species as we start to discover new problems and areas of research that we had never conceived of before. If we let AI take over all of our thinking then we are heading in the wrong direction. If we continue to ise it as the tool it is it will help us grow and advance as a species. I never expected this many people (on this thread) arguing semantics and what not. I know that not everyone has morality and ethics, but I didn't realize it was this bad. I'm afraid of the ripple effect of the agenda pushed by AI companies will have. In future and even now, they say AI has significantly progressed math and scientific research in general. There is truth to this, but the narrative has done more damage (so far) to the students, researchers, and the culture of knowledge transfer in academia. Many graduate students (I know) are having a crisis if any of their research worth it? If AI can (or will) do everything, what's the point of doing experiments and all? This will eventually deter a whole generation of curious minded students from research. I guess, only time will whether this is for the good or bad. And how good AI models get without new data from research and experiments. I think that the main thing people in this thread are missing, is that it's not about math. AI progression is very likely to affect every single thing humans can do today. Mathematicians are feeling the blow this week, especially as there was wide spread denial in that math community over the capabilities of AI over the last few years, but it's the same problem everywhere. we stumbled into a way of brute forcing intelligence with gradient descent. > Many graduate students (I know) are having a crisis if any of their research worth it? If AI can (or will) do everything, what's the point of doing experiments and all? This will eventually deter a whole generation of curious minded students from research. Those who think it's me or the machine will fail. Those who realize how much you can accelerate your research with the help of AI will succeed. > Those who think it's me or the machine will fail. > Those who realize how much you can accelerate your research with the help of AI will succeed. This is only true up until a point. If I treat a mid-sized model (say, Qwen3.8 Flash Next) like a pair programmer, then yes, it accelerates my work. But I can already see the next stage with Fable: If I give it a couple of paragraphs of spec and $50, then I can just leave the room and go wash the dishes. I learn nothing, I participate in nothing, and I bring nothing to the process. I am no longer succeeding at all. Fable's succeeding without me. Now, in this model generation, Fable starts getting sloppy after a few thousand lines. I can still build better at scale. But I don't expect AI to accelerate humans or improve our productivity for long. I can already see the first signs of a future where the AI doesn't need us for anything at all. Of course you're not going to get rich with the kind of software that LLMs can one shot these days. But that kind of software like to-do lists or basic CRUD have been saturated for over a decade, way before LLMs. People overestimate how much you can one shot, yeah a good prompt can get you 90% there but that 10% remaining often takes months of extra work. Software has always progressed this way, lots of devs back then would work on business websites that have been 99% replaced by wordpress, squarespace and instagram. I'm sure it's the same with research, you're going to tackle problems that would have not been worth the effort or outright impossible without AI. The old stuff that you'd work for months, yeah that's going to be a prompt away. > Those who realize how much you can accelerate your research with the help of AI will succeed. Yes, but, in the last week we saw an AI lab front-run[1] the research of mathematicians doing what you suggest. The lab threw something like $15M of compute at a problem and the researchers were able to spend nowhere near that. I think the authors are more concerned about that kind of asymmetry and race to publish the results. [1] - I am not going to debate whether that was deliberate on the part of the lab or if it crept into training data, etc. I don't know and don't think it matters towards the point of the authors here. This has always happened, way before AI. You'd spend months or years building and growing your business, and then Google would release a feature or product that would kill your business overnight because they can throw way more money at the problem, plus their branding. That's life. I got Sherlocked hard and it’s one of those things that when you realize it’s happening there’s nothing you can do you just gotta sit back and take it I _want_ to agree, but I fear this is too close to the old “do what you love for work and you’ll never work a day”. It didn’t lead to a lot of people having a wildly successful career, it lead to a lot of people getting burnt out, exploited, underpaid and generally disillusioned. There will be a lucky few, who have the benefit of being given the space to work alongside. The vast majority of people will (unless we change things) simply be made to take whatever the machine outputs and call it a day. Why would anyone pay you to do "your" research, when they can just cut out the middle man and ask the AI directly about whatever it is you're thinking about? So many people who are excited about AI making them more productive are, I think, drastically overestimating how much value they are adding to that process. Those who have token money will succeed. It biases maths and theoretical physics towards the rich. That one thing that was free. I think the only thing that stops this from becoming true is what Chinese and European labs decide to do. If they can keep up and keep opening their weights, then we might see some kind of democratization. But right now it looks like the gap has increased, and those groups can't replicate research that isn't published, or distill models that are internal only, or for select (very wealthy) customers. That's the crux of it. In the current ecosystem of AI model usage, it's very hard to figure this out for research. If you set a wrong foot and start trusting the model outputs, you can waste years searching for nothing. How can someone realize this? By getting proper research training, failing, and learning from mistakes. For people beginning their research, it would be really hard to make decisions to move forward. What does success look like? There will be no curiosity, no enjoyment of the process of life. All competing pleasures will be destroyed. But always—do not forget this, timcobb—always there will be the intoxication of power, constantly increasing and constantly growing subtler. Always, at every moment, there will be the thrill of victory, the sensation of trampling on an enemy who is helpless^W not also subscribed to ChatGPT. If you want a picture of the future [of math], imagine a boot stamping on a human face—forever. > Always, at every moment, there will be the thrill of victory If only though, because: > There will be no curiosity, no enjoyment of the process of life This really resonates with me. I'm early in my PhD and I'm researching a niche form of data compression and IC design. I don't use any AI at all in my research, I do it the super old fashioned way, I read papers cover to cover and sections of textbooks to familiarise myself with the field. I genuinely enjoy doing this, it's really fun to think critically about what an author wrote or how a particular approach works. But it does make you wonder, why bother? Probably a frontier model could one shot my algorithm in a day or less. It's incredibly depressing. At least I'm not forced to use it now, but I fear I will have no choice after I join academia or industry in the future. >I never expected this many people (on this thread) arguing semantics and what not. You must be new here. I used to be a PhD student more than a decade ago, and I published a paper containing a solution to an open problem. Yet shortly after my first publication I became increasingly disillusioned, because I started to think that within my lifetime AI would reach and eventually surpass my ability to solve such problems—and that we only had a decade or two left. So I started saying that it only made sense to focus on problems whose solutions would be useful immediately. I even emailed my supervisor about it, arguing that our efforts were “pointless” in the sense that AI-related problems were much more pertinent and had to be prioritised. My supervisor thought I was bonkers. I still have the email, though. Quoting myself from April 2015: > By 2030-2040 we will have enough computing power to simulate a human brain neuron by neuron. Once we manage to create a human intelligence we will be one little step away from super intelligence: just set the intelligence to modify itself and see the exponential growth in action. Our human intelligence is bounded by a number of biological factors (e.g. size of a skull) and even the smart human who has ever lived will appear to be a primitive ant to a supper intelligence (machine intelligence will also have perfect motivation). There is plenty of literature on this if you are interested in discussing this further.
>
> What does it have to do with research in pure maths? I can say that research in pure maths which won't come handy in the next 60 years is just wasted effort. The super intelligence will be able to do maths way better than humans. I believe a lot of current efforts should go into researching of artificial intelligence (or areas to do with AI) instead rather than the pure maths. I want to be proven wrong but most mathematicians I interact with are too narrow-minded to counter me and they just laugh about even contemplating the above. Frankly I am myself so perplexed that I take the above seriously, but I do and it's hurting my motivation. I'm quite curious what my supervisor thinks of that email now. I commented something similar on a bunch of other posts. The thing that scares me about a lot of the AI community in general is that their utopia is basically more frightening to me than their doom scenarios. They present this "incredible abundance" as the ultimate human endgame, but I agree, when we all end up like the humans in Wall-E, what's the purpose of it all? And then to get retorts of "it's just just rich techies that want to find 'meaning' in their jobs while millions starve in the third world". Why would we expect the most wealth concentrating technology in history to lead to mass benefits for those in the 3rd world? > I know that not everyone has morality and ethics, but I didn't realize it was this bad. This is a very disrespectful way to make a point about acting with integrity. You should consider that maybe your views on what makes something ethical or moral are not universal -- and that coming to a discussion with the assumption that your position is the only valid one is not conducive to convincing others who disagree with you. I agree. I was wrong and I had a naive world view of morality and ethics in research and academia. I now realize many people have different tolerance level for this. This story's comments are heavily astroturfed. Just compare with the comments on https://news.ycombinator.com/item?id=49639408 I actually feel like it's the other way around. The online discourse over the past ~day or so has seemed unusually irrational to me for a technical audience. Commenters making emotionally charged claims of wrongdoing that appear inconsistent with the published claims without justification of the discrepancies. Granted you might well doubt openai's version of events but there's a general expectation of clear evidence when advancing claims of malfeasance. I identify as neither mathematician nor "maker of things people want" (coder, hacker, engineer). But having friends who identify as those kinds of professionals, let me make some observations. To use a metaanalogy from chess (once again), mathematicians play the opening game, and builders play the end game. AI is sort of a middleman connecting human understanding to applications. I think there's a Technical argument to be made that openAI is a threat to the game itself. For example, could it have produced the navier-stokes counterexample without human inputs? since it seemed to have used the much gossiped research strategy "C" and "D", you can't absolutely be certain that Son of Astra (son of altman?) was magicking an unknown unknown from nothing (sorry to cue Rumsfeld). You have got to wait for the other five problems to be solved after general boycott Subpar PR engine of the OpenAI leadership might kill the pipeline of inputs that they won't admit they still need in this dreamtime before "recursive self-improvement". You can call that emotional. Personally I would rather accuse mathematicians of "preferring local models that believe in the usefulness of unidentifiable individual contributors, and the uselessness of named generalist managers (ie the prompt writers at oAI)" Big man tlb likes to say that science might be dead but engineering is just getting started. Navier-Stokes is the hammer of the nail in the science coffin. It kills science by killing the prestige of science. The engineers have to imagine that it's likely they will now get all their design ideas from the hypothetical future datacenters. > The engineers have to imagine that it's likely they will now get all their design ideas from the hypothetical future datacenters. At the current rate of advancement that phase will last, what, all of 6 months if we're lucky? To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of these models being capable. Even without AI labs spending millions of dollars to solve millennium prize problems, there are plenty of other people who will use them to pick low hanging fruit. I don't think any social solution is going to make things go back to the way they were, where you could share your progress towards a famous open problem without risking someone "scooping" you within a couple of days. I think that the most likely outcomes are either mathematics becomes more secretive, or there is a more deliberative approach to assigning credit than who was "first" to solve some problem. In the former case, this may slow down progress, and in the latter case, this could mean that credit would become more subjective, and be a continual source of controversy. The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are investing these resources primarily as a marketing exercise. There is no near term commercial value to a 100 page Lean proof of blow up in an extreme special case of Navier Stokes, besides the bragging rights. As the statement says any commercial value in this stuff comes a very long time later after new insights and techniques have been digested, integrated into the mathematical canon, expressed in ways that don't take a lifetime of study to understand, etc. (things that AI is not yet capable of doing itself). The bragging rights, on the other hand, are massively valuable. There is a mystique to maths that makes "our AI solved a Millenium Prize problem" an irresistable headline for a company like OpenAI. What the mathematicians are saying is stop pouring resources that most mathematicians can only dream of accessing into projects that are actively damaging to their field. They face a massive challenge of figuring out how maths can evolve in the face of this new technology, and this is not helping. What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I feel like the mathematicians working on these should know about them, but on the other I feel a bit like a barbarian who suddenly finds themselves sacking Rome. I'm not a mathematician but it seems to me that if all it took to solve the problem was an enthusiast level understanding of the domain and a few hundred dollars of tokens then the result probably isn't that valuable. Even assuming you are the first person in the world to solve it, these kinds of LLM-friendly problems that are now easy to solve and easy to verify will almost certainly be picked off by one person or another in the near future. It's also possible that the result is already known and you just weren't aware of it. It's easy for someone outside of a field, or even one steeped in it, to not be aware of certain solutions. sounds a bit like cope. Crouzeix's conjecture was solved exactly under these circumstances and I wouldn't describe it as "not that valuable". In any case, AI capabilities will increase dramatically over the next few years while human math capability will not. That means that there's a fixed target regarding whatever is currently considered a "serious math problem" and its difficulty level. Soon the average problem solved with a few hundred dollars of compute will be at that bar. > while human math capability will not. I actually partially disagree with this. What happened to all the excitement about Intelligence Augmentation (IA)? Now it's AI instead of IA. I think there's so much untapped potential for augmenting our intellect with the likes of https://dynamicland.org and https://folk.computer, as well as the work that's been going on in college math education, things like Lean, etc. I think the only reason human math capabilities haven't expanded that much is a failure of our imagination, not our potential. > I am at a loss about what to do with these results. I would recommend publishing them to Palomar (https://palomar-registry.org/) - I have no affiliation, this is an online registry of Lean-verified proofs created by Terrence Tao. I have submitted a proof there that's also minorly important in an extremely niche field. Anyway, I feel like it's a good place to dump AI slop lean proofs because the main point of the registry is that it verifies that: 1) your Lean challenge statement is the same as what you informally state you're trying to prove; 2) your Lean proof actually compiles. This could be useful to future AI slop researchers who want to know if a given result has already been formalized, and they may be able to mine some lemmas from your work. Also, it's good to know for the field in general what has been proven. I'm fairly certain you can set your publishing name to be whatever you want, so you could set it to be just the word "Anonymous", or the name of the model you used. It is interesting isn't it. You asked for a painting. A robot made the painting. You looked at it and said, "well, I guess it's good. Should I put it online or something? Dunno. Hey Fred, what do you think of this?" Meanwhile, your next door neighbor spends their entire life developing their understanding of life through art. They "understand" (maybe not in a way they can articulate) art. You go next door, you look at their painting and say, "well I guess it's good." But you also understand that your neighbor is just like you, and maybe you are a painter in another way. I find it strange that, people can't see that, we don't need to solve hunger and poverty and work balance, and etc, by a round-about make-super-intelligent-AI. We could just solve it. It's pretty obvious how to, as well. We can all be painters, if we put restrictions on the psychopaths. How do you know the proofs are correct? The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private. They're valid. It's really tough to come to terms with it but making academic contributions in general from the outside (with or without AI tbh) is not often welcome and the whole process feels very gate-kept. (academic.) Unfortunately the overwhelming majority of outsiders are missing core knowledge (or are cranks), so the optimal prior from a time management perspective is to ignore them. AI just makes engaging more costly because there’s more volume and it’s harder to get signal on whether they know what they are talking about. If that's the case, that makes me much less sympathetic, even though I can understand how it's very disturbing to see the field suddenly changing like this. I mean, let's say you spun up a swarm of agents to rewrite a large component of a well used open source library to be memory safe. You could dump it in a big PR and walk away (we all know how that would go), or you could try engaging, see if they're interested, write something up and see where it goes. The biggest problem is, IMO, drivebys uninterested in actual results, just getting a check mark, and the equivalent of dropping a 200k line PR on people and expecting them to be interested and do the work for you. These are things many on HN are familiar with and know how to do better :) > and the equivalent of dropping a 200k line PR on people I can understand why the community is pissed. So now, lean proofs can be churned out at scale, and the community is left to decipher all of that slop into human understanding. There are bad actors with misaligned incentives coming in with drive-by proofs upending what the community holds dear which is to practice and propagate the art. I applaud them for this declaration. To re-align incentives the following could happen. AI slop lean proofs are dumped unceremoniously into a lean dumpster, and what gets rewarded are results that could digested into human understanding - via the already followed human review process. Prizes are not given to lean proofs since anyone with sufficient compute can churn them out. It depends. If you are trying to understand better the field, then do a good write up of the proofs so that people can learn from it. If you want to earn the respect of people because you found interesting proofs. Then do a good write up of the proofs so thst people can learn from it. If you want to plant flags and pollute peoples minds. Then please publish it anonimously, no one wants to correct LLM slop for you. Probably we should build a repository of AI slop proofs that are only allowed to be publish anonimously. That way people may be more inclined to work on it because they would feel like they are cleaning your house for free. Maybe I'll end up doing the write ups pseudonymously. I have taken care to make sure the results can meaningfully contribute to field but I don't want to plant flags or really receive credit of any kind. I just think they are interesting. I like my current life and don't want to get dragged into the current fracas surrounding the use of AI in math. If you have taken care, then share it with the community. People will be thankful and happy. The problem is with people that may do it without contributing to the community. If this was limited to just three results, I would agree with you. But those three are just the ones I've managed to verify myself. The list of unverified results is quite a bit larger. The field I've been investigating is not large. Even if I were to take the time and care to beat the interesting results into something meaningful, I'm afraid the pace at which I'm able to produce these results would not be well received. That solution (stop pouring resources in to proofs, stay in your lane) works today. How does it work 5, 10, 20 years from now? The software and hardware advances will continue. > primarily as a marketing exercise Like the mathematicians working on famous problems in private until they could claim full credit for something interesting wasn't also a marketing exercise for their own careers. The commercial value (or lack thereof) of a proof doesn't depend on whether it was done by a human or a machine. These mathematicians dedicated their life to math and were working for a long time to achieve the pinnacle of their careers. OpenAI just burned millions of dollars over a weekend after hearing that someone else was close to solving the problems. Their interest was in their AI system more than the actual math problems. Don’t you see how that’s different? I see how it can be devastating to their ego, but no, I don't see a particular difference in a company spending money for clout vs. a person spending time for clout. The underlying motivation is the same. Do you really think people dedicate their life to mathematics for clout? If clout was the goal I don’t think becoming a lifelong mathematics academic would be the first step for many fairly strong mathematicians, the career calculus is fame and status (mild though it may be) through mathematics or anonymity but financial reward in tech or finance. Yes, clout by becoming a lifelong academic is in fact rational for some and part of their motivation. Of course they really like what they do as well, but earning the respect of the peers they know are also respected by a large swathe of society is very important. I think you’re right that some of the angst here is due to a fairly insular community having its culture disturbed by commercial forces. Yeah that’s totally fair! I guess that type of “clout” feels different to me. Wanting to be validated by peers for your talents in a niche field vs. using millions to try to solve a math problem that you don’t really care about with AI to market the gigantic company you work for. Yeah bro, same for probably the majority of this site that write software for a living and/or hobby. Sorry I’m not entirely sure what you’re trying to say How good were you at those “A is to B as C is to D” SAT questions? No need to be rude. I didn’t want to misinterpret when responding. I can see how what is happening to mathematicians is similar to what is happening to coding. I’m not sure what your broader point is? Mathematicians shouldn’t be upset? Coders should? Something else? The point is that nearly every white collar worker is in the same boat right now, and the majority of them probably have already had much more profound impacts to their fields. So yeah, we can certainly imagine what it’s like for mathematicians.
tmhn2 - 8 hours ago
GPerson - 2 minutes ago
stabbles - 7 hours ago
318274 - 7 hours ago
mna_ - 7 hours ago
psvv - 6 hours ago
jasonfarnon - 3 hours ago
cgio - 2 hours ago
stabbles - 5 hours ago
onetimeusename - 34 minutes ago
Xirdus - 4 hours ago
vouaobrasil - 4 hours ago
fidotron - 5 hours ago
mb7733 - 5 hours ago
TheOtherHobbes - 4 hours ago
fidotron - 5 hours ago
saghm - 4 hours ago
tomrod - 37 minutes ago
lacunary - 4 hours ago
charcircuit - 5 hours ago
debatem1 - 7 hours ago
ArcHound - 6 hours ago
debatem1 - 5 hours ago
Quekid5 - 6 hours ago
VulgarExigency - 5 hours ago
ArcHound - 5 hours ago
jacobolus - 4 hours ago
magicalist - 7 hours ago
Quekid5 - 6 hours ago
robotpepi - 6 hours ago
Bourget - 6 hours ago
robotpepi - 6 hours ago
flatline - 5 hours ago
jeremyjh - 4 hours ago
phoghed - 4 hours ago
3ash14 - 6 hours ago
coderenegade - 4 hours ago
tomrod - 33 minutes ago
tzumaoli - 7 hours ago
alkyon - 6 hours ago
genxy - 6 hours ago
falcor84 - 5 hours ago
_superposition_ - 3 hours ago
alkyon - 5 hours ago
GPerson - 6 hours ago
alkyon - 5 hours ago
zahlman - 5 hours ago
amelius - 5 hours ago
evenhash - an hour ago
bayindirh - 5 hours ago
Ethan_Barry - 4 hours ago
bayindirh - 4 hours ago
amelius - 5 hours ago
num42 - 7 hours ago
318274 - 7 hours ago
SavageNoble - 6 hours ago
breezybottom - an hour ago
SavageNoble - an hour ago
cubefox - 7 hours ago
ksoped - 7 hours ago
cubefox - 7 hours ago
SpicyLemonZest - 6 hours ago
glitchc - 2 hours ago
SpicyLemonZest - 14 minutes ago
bluecheese452 - 5 hours ago
dbmikus - 4 hours ago
If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :) (A) it furthers human knowledge
(B) it gets used in applied sciences, engineering, etc.
coderenegade - 42 minutes ago
SpicyLemonZest - 4 hours ago
jrecursive - 6 hours ago
genxy - 5 hours ago
darkstarsys - 5 hours ago
onetimeusename - 6 hours ago
NateEag - 5 hours ago
onetimeusename - 30 minutes ago
curt15 - 4 hours ago
visarga - 6 hours ago
tmhn2 - 4 hours ago
_superposition_ - 3 hours ago
unknownunknown7 - an hour ago
CamperBob2 - 5 hours ago
fph - 5 hours ago
sweezyjeezy - 4 hours ago
Timwi - an hour ago
roywiggins - an hour ago
kzz102 - 4 hours ago
embedding-shape - 4 hours ago
kzz102 - 3 hours ago
cevi - 6 hours ago
well_ackshually - 7 hours ago
tmhn2 - 7 hours ago
ksoped - 7 hours ago
SJMG - 7 hours ago
deanCommie - 6 hours ago
zozbot234 - 6 hours ago
kfse - 5 hours ago
12_throw_away - 3 hours ago
mk_stjames - 6 hours ago
(from, 'The Elements of Programming Style') Everyone knows that debugging is twice as hard as writing a program in the first place. So if you're as clever as you can be when you write it, how will you ever debug it?
antonvs - 5 hours ago
overfeed - 6 hours ago
antonvs - 5 hours ago
ksoped - 7 hours ago
tmhn2 - 7 hours ago
famouswaffles - 7 hours ago
demibabs - 6 hours ago
famouswaffles - 6 hours ago
pizzly - 6 hours ago
_superposition_ - 3 hours ago
matco11 - 6 hours ago
coderenegade - 3 hours ago
sghiassy - 6 hours ago
genxy - 6 hours ago
DoctorOetker - 5 hours ago
genxy - 4 hours ago
citizenpaul - 4 hours ago
dmoniz - 3 minutes ago
pks016 - 3 hours ago
gpt5 - 3 hours ago
teravor - 2 hours ago
should they not be deterred? > Many graduate students (I know) are having a crisis if any of their research worth it? If AI can (or will) do everything, what's the point of doing experiments and all? This will eventually deter a whole generation of curious minded students from research.
redox99 - 2 hours ago
ekidd - an hour ago
redox99 - 25 minutes ago
trimbo - 2 hours ago
redox99 - 39 minutes ago
AndrewKemendo - 19 minutes ago
FridgeSeal - 2 hours ago
munificent - an hour ago
immmmmm - 2 hours ago
coderenegade - 31 minutes ago
pks016 - 2 hours ago
timcobb - 2 hours ago
kibwen - 2 hours ago
timcobb - 42 minutes ago
myng111 - 42 minutes ago
lbrito - an hour ago
afiodorov - 27 minutes ago
hn_throwaway_99 - 23 minutes ago
LordDragonfang - 2 hours ago
pks016 - 2 hours ago
octoberfranklin - 3 hours ago
fc417fc802 - 2 hours ago
oliculipolicula - an hour ago
fc417fc802 - an hour ago
jeremysalwen - 8 hours ago
omnicognate - 8 hours ago
causalmodels - 7 hours ago
rurp - 5 hours ago
pickleRick243 - 3 hours ago
smj-edison - 3 hours ago
tejstead - 5 hours ago
bubblegumcrisis - 5 hours ago
lasersox - 7 hours ago
causalmodels - 6 hours ago
ardme - 6 hours ago
gammarator - 4 minutes ago
FartyMcFarter - 5 hours ago
magicalist - 6 hours ago
bwfan123 - 4 hours ago
youoy - 6 hours ago
causalmodels - 6 hours ago
youoy - 5 hours ago
causalmodels - 5 hours ago
sobellian - 7 hours ago
ralph84 - 5 hours ago
paulhebert - 4 hours ago
ralph84 - 4 hours ago
paulhebert - 4 hours ago
pickleRick243 - 3 hours ago
gammarator - a few seconds ago
paulhebert - 39 minutes ago
phoghed - 3 hours ago
paulhebert - 3 hours ago
phoghed - 3 hours ago
paulhebert - 3 hours ago
phoghed - 3 hours ago