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Tao: Open math problems being non-renewably mined by AI

• twotwotwo 25d ago
  This is worsened by OAI/Ant's strategy of grabbing the glory and running rather than spending effort trying to to advance understanding of math. Tao, who is quite sophisticated in use of AI, has said a lot about this, including in meme form: https://mathstodon.xyz/@tao/117068266026618494 https://mathstodon.xyz/@tao/117068266026618494 The AI labs' approach to math is immature in a way they can't get away with in coding. In coding, they realize that a pile of code that technically works is not enough: they need the code output to be a foundation to build on, and they need their agents to work well with humans which means explaining things in a way that makes sense. In math, their goal seems just to be to exploit mathematics' reputation as full of hard problems with a general population that can't tell a pile of Lean from a good proof. OpenAI pretty much said this work is just to show off at the end of the post. Anthropic said their FLT formalization is a research artifact they do not intend to clean up or improve in any way. Besides uniting mathematicians in irritation at the labs, the other flaw with this strategy is that it ignores that organizing knowledge is part of intelligence, much like not just producing a mess that runs is part of programming. You can write a proof that uses algebraic geometry because someone organized what could have been a bunch of disparate ideas (or fragments of a Lean repo no one will read) into a toolbox where an expert can find the tool they need. I hope they change tack. Perhaps instead of making an explicit strategy of taking the credit from mathematicians but doing little for actual understanding, they could let some math departments at their swarms or best models, ask for a bit of acknowledgement, and hopefully they approach it by trying to write good papers, simplify, etc. rather than just rushing for headlines. (Tao's post about digesting an LLM-generated proof https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/ https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the... is an interesting read for a sense of what he means by 'digestion'.) On that last note, it's also important (Tao's also noted) for the mathematical community to properly value digestion and organization of results, so that given the incentives of mathematics and availability of new tools you end up with good papers and textbooks and so on, not just mathematicians taking the labs' current role of pushing incomprehensible-even-to-specialists proof code to repos.
  • kccqzy 25d ago
    Besides Sendov’s Conjecture, Terence Tao has also shared his AI-assisted digestion of the counterexample to the Jacobian conjecture. In simple words, digestion just means full human understanding of the results. It could come from understanding the result from a different perspective, or perturbing the result and seeing what breaks.
    • twotwotwo 25d ago
      The Jacobian one is great, and fits here -- 1) the counterexample came out as a tweet of a single expression which seems exceptionally hard to turn into something sensible, which crystallizes the lab's approach; 2) it links (like the Sendov post) to a chat transcript showing a little of what was involved in untangling it (though of course all that went into asking the right questions is invisible!). For other folks, the post: https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/ https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the... The transcript: https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed56 https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed...
• turtleyacht 25d ago
  If proofs are tropes, explanations are stories. There won't be an end to stories.
  • vouaobrasil 25d ago
    Actually there will because if you've actually ever spent time doing math, you only really get to that level of truly understanding and appreciating the stories if you've actually done the hard work yourself, which in turn will be economically infeasible due to AI. The analogy is interesting but incomplete and misleading.
    • CamperBob2 25d ago
      you only really get to that level of truly understanding and appreciating the stories if you've actually done the hard work yourself, which in turn will be economically infeasible due to AI The thing is, nobody has time for that. Look at Mochizuki's work. It takes years of hard labor by high-level mathematicians to come up with stuff like that, and years of hard labor on the part of other mathematicians to validate it. The low-hanging fruit in math has all been picked, AI or no AI, and Tao doesn't seem to acknowledge that. The mathematics community needs better tools or they're out of business anyway. Now they're getting those tools... and bickering and complaining about it?
      • vouaobrasil 25d ago
        I agree that the low-hanging fruit has largely been picked. But then I think we should acknowledge that and stop innovating, or just work less on new solutions and more on clarifying old ones, and start to work on degrowth rather than useless problem solving. Because I really don't feel that any of this is really necessary or beneficial for the human race in the long-term.
    • gpm 25d ago
      I've actually spent time doing math and literally everyone I know who knows math learnt it by reproving things that people proved before them. I don't see why AI proving things makes this form of learning any more economically infeasible than the field of mathematics already is - and since it was apparently economically feasible before AI I expect it to stay that way.
• vessenes 25d ago
  That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle. Mathematics has always been highly competitive.
  • enraged_camel 25d ago
    [flagged]
    • usrnm 25d ago
      Do you have a real argument to make rather than just appealing to authority?
      • enraged_camel 25d ago
        So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority? Get outta here.
        • magicalhippo 25d ago
          Knowing the math that was developed through history, and knowing how that math was developed and the circumstances around it are two fundamentally different things. Clearly Tao knows the former, but apriori that does not imply he knows the latter. Not saying he doesn't, just saying one does not imply the other. Even if you go back and read the original papers, you'll miss all that which happened beyond the page.
        • lo_zamoyski 25d ago
          > Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? If Tao has a knowledge of the topic (which he does), then it isn't by virtue of being a mathematician per se, but by virtue of an interest in the history of mathematics (which he has). Knowledge of math is enormously helpful here, but it does not imply historical knowledge.
• ltbarcly3 25d ago
  I think he's suffering from a sort of static-universe fallacy. People aren't going to keep doing what they are doing, but secretly. What is going to happen is a complete revaluation of things like "finding a counter example to a famous problem". Even if someone finds a solution to a problem like this with pencil and paper, nobody will believe it, and they will assume that there was an AI involved. Further, sitting and doing math with a pencil and paper will no longer be a reasonable strategy to build a reputation or career, beyond the benefit a mathematician gains to their own intuition and skill. People who work hard to build intuition and also use AI effectively will dominate the field. In a world where everyone is using AI, the open problems that remain will be the ones that are AI resistant. This is no different that how things work now, mathematicians wait until they are fairly confident someone won't rapidly solve their problem before they start talking about it. They will do the same thing in the future, except in the future AI will be part of the toolset they use decide if they are ready to share yet or not. Edit: Ok I believe I was generally right here, but I just read the details of what OpenAI did. They didn't solve a longstanding problem, they got tipped off to an approach a mathematician was using and would likely result in the solution very soon and they finished it first. If this turns out to be true I think my take above is not correct, in the short term people will have to stop sharing updates because otherwise openai will dishonestly race to finish their work.
  • dev_dan_2 25d ago
    > If this turns out to be true I think my take above is not correct, in the short term people will have to stop sharing updates because otherwise openai will dishonestly race to finish their work. Which I don't see a reason for Anthropic and "Open"AI not to, given their not so stellar track record with IP of individuals/entities-that-are-not-rich-enough ;)
  • senordevnyc 25d ago
    People who work hard to build intuition and also use AI effectively will dominate the field. This will be literally every field, sooner or later, at least until the human and their intuition is just slowing the AI down. There’s no scenario where humans without AI beat humans with AI in the long run, unless there are fields where the “alien intelligence” somehow hurts more than it helps (like artistic pursuits perhaps?)
• olalonde 25d ago
  Isn't it safe to say that all famous unsolved math problems will get a "massive amount of AI-powered effort" pointed at them regardless?
  • tzone 25d ago
    While AI companies have almost infinite money, they still don’t want to blow million dollar budgets on problems if there isn’t high likelihood that it will be successful. But within next 10 years as costs drop significantly and even more improvements are made, yes it is very likely that almost every single existing math problem will get a serious AI cracking done on it
  • curt15 25d ago
    A "massive amount of AI-powered effort" costs a ton of money. What's the return on investment for these frontier labs? Do headline-grabbing successes in mathematics translate to expected *profitability* in disciplines with more immediately quantifiable economic value.
• gradus_ad 25d ago
  >"While it may be technically infeasible to completely prohibit the use of automated tools to perform indiscriminate solution extraction, I believe that we can still designate many classes of problems as being desirous of a careful analysis that not only solves the problem, but identifies insights from the solution process, and learn more about the difficulty landscape for nearby problems, and for which raw solutions without such analysis would be of negligible or even negative value for these purposes." Not sure I agree with this. AI generated proofs can still be analyzed and mined for useful insights. I suppose he's saying the process of banging our heads against the wall on a problem can itself yield useful insight? But what is stopping us from analyzing a proof after the fact. And if we can generate many different versions of a proof that should help us develop a much deeper understanding of the problem than we would have without being able to perceive the "proof landscape"...
  • SpicyLemonZest 25d ago
    He's saying that in such a scenario, almost all of the value is located in the analysis and just dumping the proof has "negligible or even negative value". (The negative value would occur in the cases where the proof doesn't contain enough information to reconstruct what insights would have led a person to it.)
  • cattenwallen 25d ago
    I think you're misunderstanding the point of math problems. Mathematics is as much a process as it is a result. This is why even from early on, relatively rudimentary mathematics questions you are graded by your capacity to correctly achieve the desired process to the answer than getting the answer correct. The risk here is that AI generated proofs removes the process part of mathematics, where actually interesting concepts live (because then you can apply novel concepts to other unsolved problems and then thereby unlock new concepts that way...) Sure you can kind of try to reverse-engineer it but you lose the entire intuition and "we tried applying it in X, Y, Z ways and it didn't work" intuition, because even the non-working process can teach you about how not to apply the working process to novel problem spaces. Basically: Tasting a delicious soup doesn't tell you how to layer the flavors, but if you want to be a good chef, you better be learning flavors more than you learn dishes!
• ozgung 25d ago
  No matter what happened this must be a wake up call for all of us. We’re basically sharing everything we have with these companies/AI systems. This is wildly different than a human wiretapping our private messages. Because it is systematic and automated in an astronomical scale. There is no real privacy in this new world. Law? I think “National Security” is a good enough excuse to screen anything constantly, including foreign researchers in case they are close to a breakthrough.
  • GolfPopper 25d ago
    >We’re basically sharing everything we have with these companies/AI systems. My sense of the word 'share' is that it traditionally involves agency by all parties involved. There are a lot of words in English for describing taking things without permission and profiting thereby - words like piracy, banditry, and larceny.
    • crisnoble 25d ago
      Next you will try to tell me that these companies built upon nothing but piracy, banditry and larceny would continue to commit piracy, banditry or larceny.
• johnsmith1840 25d ago
  I mean, hasn't it always been this way? If something valuable is within reach and you disclose it, someone else might reach for it? Just because the length of the arm is longer with an AI org doesn't mean it's somehow fundamentally a different system. The future is that if you don't use AI your work is a lot easer to reach against someone else who has it. That dude hand writing code with punchcards can be lapped by a 20yo with python, what's different?
  • calf 25d ago
    The difference is no one writes punchcards so the comparison is inapt. It is more like supposing AI eats everything humans attempt to do. They will take your work as you are working on it, any interaction at all. It is meta-plagiarism, on another level.
    • johnsmith1840 25d ago
      AI didn't "take" anything. An openai researcher did? The solution is also different to theirs? Literally no evidence of plagarism?
      • opello 25d ago
        No evidence until there's an answer to the question of if prompt data from the other researchers was used to train the internal model. I think the reasonable ethical question to consider when a company has an incentive to prove its value, and learns of the state of the art of a flashy research topic being close to a solution, and then throws loads of resources at trying to solve it first. I agree that "AI" didn't "take" but it's not an incomprehensible shortcut of criticism of the aforementioned behavior, not that precision should be avoided here.
        • johnsmith1840 25d ago
          Ok so if no plagarism has occured here in any sense then there's no discussion here? I agree though if they did plagarism it's really really bad for OpenAI. They would instantly have evaporated all remaining good will to gloat over a stolen discovery.
• _alternator_ 25d ago
  This series of posts by Terry Tao is a direct response to the Navier-Stokes results (multiple results!) from the last 24 hours. The question is what is left after the levelling of mathematics, in all its senses, occurs? How can you protect a field that's under this much pressure in the next 6 months? > [I]t is now the identification of a promising problem which is the scarce and precious resource. We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential.
  • calvinmorrison 25d ago
    > How can you protect a field that's under this much pressure in the next 6 months? Sounds like they're going the way of the DoDo. better take that PhD, migrate to the new world and become a tuktuk driver.
  • ModernMech 25d ago
    If math is solved then move to an area that’s not. Why do fields need “protecting” from ai?
    • dgellow 25d ago
      Have you read his tweets?
      • ModernMech 25d ago
        yes but the tweets don't really address why the field needs to be protected instead of adapting and evolving. And to reply to the sibling since I hit my comment limit and I'm going to probably forget about this conversation until tomorrow: But our situation before 2023 was one in which we had an endless abundance of solutions and ideas. I understand that AI can generate bad ideas faster than we can discern them, but we already have tried and true mechanisms to filter good ideas from bad (e.g. the scientific process), why can't they be adapted?
    • vouaobrasil 25d ago
• woodgala 25d ago
  It sounds like a fancy way of saying kids will forget how to do math if they use calculators. The flattening of the space makes it hard to find new problems deemed significant? Maybe that went over my head, I’ll concede that point.
  • fwip 25d ago
    What? No, it's nothing like that. It means that if you have a critical insight and you share it out loud, somebody with no particular mathematical inclination can just spend lots of money to steal the credit from you. It shifts power further from the worker toward those with capital.
• program_whiz 25d ago
  Timing is everything https://nonlineartransform.substack.com/p/ai-swarms-timing-is-everything https://nonlineartransform.substack.com/p/ai-swarms-timing-i... Article arguing math is the next "human calculator".
• 20k 25d ago
  We're having to rediscover in real time the extremely hard way, why enabling mass theft is so incredibly damaging to society. This is literally why we need a functional copyright system If theft becomes more profitable than genuine creation, then nobody will create anything. Then there's nothing to steal, at which point all progress collapses
  • CamperBob2 25d ago
    This is literally why we need a functional copyright system To block progress. Got it.
    • 20k 25d ago
      This is the literal opposite of progress: stealing from people genuinely creating, and stealing the money they should earn
      • CamperBob2 25d ago
        Funny, the stuff that was stolen is still there. A strange kind of theft. Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon.
        • majormajor 25d ago
          > Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon. Frankly it's more of an insult to the "hacker" name to be apologising for big companies profiting off of frontrunning existing work for PR purposes, if the claims about piggybacking on human-directed efforts/prompting are true. Being pro-copyright in order to protect the work of an individual from being reconstituted into the corporate machine is VERY hackery. Novel use for an existing tool, to fight the dominant system. (Of course, we're on a so-called "hacker" site hosted by a company run by squarely-establishment individuals acting in an extremely un-hackery-field (investing), so the irony here has been at least one layer deep since the start.)
• olalonde 25d ago
  Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.
  • lalalanananana 25d ago
    It's possible but the approaches these tools take are usually verbose and strange. Think about it like anything else llms do. Even when the picture is right and there are only 5 digits on each hand all the textures are off and so is the lighting and postures. Or in code, the code is always way larger then it needs to be and tightened up strangely with weird loose ends. Or in writing weird idioms, words, structure, and a weaselly way to turn 3 sentences into 8 paragraphs. People usually use these tools in math and science to find an answer. Then often they will work it back using more sane or human pathways. So it's shareable or even beautiful. Knowing the answer has value. But, often in math the best thing was how someone got there.
  • _alternator_ 25d ago
    Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of Navier-Stokes will probably take a similarly long time. In the mean time, it looks like all open problems will be solved (or proved that they can't be solved). It's not that the horizon is expanding because of this. It's more like a forest getting clear-cut.
    • layman51 25d ago
      This reminds me of the time an AI was taught how to play a racing sim game (Gran Turismo if I remember correctly). The AI was able to race its car very well, but it took a lot of risks that a human player probably would not. A human player might be able to copy the approach the AI took, but they would probably crash. Going back to chess, I think the situation is similar where you can’t expect an amateur player to get better by trying to play like a strong engine. I think even professional chess players mainly use engines to prepare or memorize variations that are counterintuitive for their opponent. In other words, getting into situations that look wild, but that part of one player’s preparation. I’m not sure how it is in math, but in chess, it seems like top players can play just like engines when they are in “normal” positions, so that is where I get a bit confused as to where the direction of insight is coming from because it’s been my view that AI is able to make leaps that we would never think of taking and I’m not sure that anyone could actually learn how to do that on their own unless they were willing to keep failing over and over.
• colinhb 25d ago
  Seems like in current cultural and economic context, short term extraction is what we’re going to do > In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained.
  • CamperBob2 25d ago
    The "ecosystem" is dead. Tao should be thinking about what will replace it. I don't understand why he's taking this tack.
    • deleted 25d ago
      [deleted]
  • mizzao 25d ago
    Is there an analogy here to the phenomenon that senior {engineers, designers, PMs} are now able to be insanely productive with AI, but it's also very hard to train junior folks to develop the sense of judgment that senior folks have?
• dvt 25d ago
  I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession. Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.
  • BeetleB 25d ago
    Mathematicians will be less likely to work on a problem if there is a solution - even an incomprehensible one.
    • dvt 25d ago
      > Mathematicians will be less likely to work on a problem if there is a solution Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle existed which could answer any question truthfully. Let's ignore the mechanics of this for now, but it could say things like "the Riemann hypothesis is False" or whatever and we would take it as gospel. Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? I genuinely don't think so.
      • _alternator_ 25d ago
        I mean, the oracle doesn't really seem so hypothetical right now. And clearly it's going to drastically change these fields, and mathematics, particularly pure mathematics, must change most of all in order to adapt to the existance of a math oracle (or something close to it).
      • nafey 25d ago
        I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems. FWIW this is my understanding of his argument and I am not a mathematician.
• bwfan123 25d ago
  It is now clear to me why the AI labs are sponsoring these mathathons: https://mathathonchallenge.com/ https://mathathonchallenge.com/. They are basically crowdsourcing human researcher data to get access to promising directions possibly later to scoop others.
  • throwaway1707 25d ago
    Not so dissimilar to my first comment on this site (which I got piled on): https://news.ycombinator.com/item?id=48959395 https://news.ycombinator.com/item?id=48959395 Except way more nefarious than I expected
• gpm 25d ago
  See also his previous thread from before the result was published (and before he knew it was coming [1]) on how a to this problem seemed increasingly likely to be solved by AI in a way that caused us to miss the insights that would traditionally be associated with solving it: https://mathstodon.xyz/@tao/117207849921390904 https://mathstodon.xyz/@tao/117207849921390904 [1] https://mathstodon.xyz/@tao/117219101339291693 https://mathstodon.xyz/@tao/117219101339291693
• animanoir 25d ago
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• arjie 25d ago
  Well, we name conjectures after the conjecturer not the (dis)prover so there is some incentive to be the guy who comes up with a hard problems. It is curious that we haven’t had something like this improve OR etc. problems. Perhaps not glorious enough.
  • p-e-w 25d ago
    > Well, we name conjectures after the conjecturer not the (dis)prover That’s not universally true. Some conjectures are renamed after being proven. For example, Fermat’s Last Theorem is now sometimes called the Fermat-Wiles Theorem, the Taniyama-Shimura Conjecture is often referred to as the Modularity Theorem now, etc.
• dakolli 25d ago
  [flagged]
  • perching_aix 25d ago
    alright, i'll bite: what real work did you put out there that has improved the lives of regular people in the past one year? (without the use of ai, needless to say)
• jfengel 25d ago
  I didn't realize that open math problems were a finite resource. I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest. Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.
  • pitchlatte 25d ago
    his whole point is that specifically problems that have been held as important by consensus in the field are a finite resource. obvious example being the Clay millennium prize problems. seems like they function to shape the direction of future research into useful directions. which is to say, the process of developing a solution itself generates more useful problems. of course thrrr are tons of problems once you remove this social consensus based filter. if i’m not mistaken Ramanujan left a book of dozens of unproven theorems, for one quick example. i don’t think that that has opened up dozens of fields of mathematical research.
    • gowld 25d ago
      > the Clay millennium prize problems augmented Hilbert's problems of 1900. Surely mathematicians are creative enough to ask new questions? If not, then the next set of challenges will be to find questions to ask!
      • dgellow 25d ago
        Did you read Tao‘s tweets? That’s what he addresses
  • _alternator_ 25d ago
    I think "close to completion" is not the right framing. Creating good open problems was an achievement because these problems often sit at the edge of known techniques, and solutions require inventing "new math". It's hard to find these problems, and they take decades to mature as they withstand scrutiny by many people. In another comment below, I likened this to clear-cutting a forest. Growing the forest takes a lifetime; destroying it could happen in the next few months.
• thymine_dimer 25d ago
  Doesn't this just suggest that the next frontier for powerful AI models is to ask challenging questions, not simply solve them? Terry even says this: "In fact, it is now the identification of a promising problem which is the scarce and precious resource." The creativity and insight needed to ask a question that Terry gets excited about is the next step. Perhaps OpenAI should create a set of challenging questions and offer a prize to solve them.
  • roywiggins 25d ago
    If AI can generate questions and then answer them, what are the people for?
    • gowld 25d ago
      If humans can shovel dirt, then what are the ants for?
      • roywiggins 25d ago
        https://en.wikipedia.org/wiki/Decline_in_insect_populations https://en.wikipedia.org/wiki/Decline_in_insect_populations
  • qlte 25d ago
    The incentives are massively skewed towards the AI labs investing their massive amounts of compute into being the first to solve an outstanding problem. It's a marketing game for them, any societal benefits are secondary. Winning a prize is going to get headlines and feed into the "AGI soon, machine replaces another career" narrative they crave unlike coming up with some (possibly) interesting problems.
  • pictureofabear 25d ago
    I think the problem with AI asking questions is that it will ask questions that are interesting to it but not necessarily us. AI, as a model, will never be a perfect copy of a human. It will always be a simulation, and thus to some extent, will ask questions that humans find irrelevant and solve problems that humans find irrelevant. For anyone facing an existential crisis on AI, your ace in the hole is your humanity. Only you have it, and only you will be the best judge of what is good and interesting (to a human at least).
• jujube3 25d ago
  We're running out of math. Maybe the president needs to establish a Strategic Math Reserve.
• esafak 25d ago
  It's the same pipeline problem coders have been talking about; once AI does all the work, how are people going to get the experience necessary to take part productively?
• coliveira 25d ago
  This to me is another level of dishonesty. Imagine if a company producing math software starts to hear "rumors" someone is using their software to prove an important result and start massive runs of that software to beat the team. That may not be illegal per se but it is incredibly deceitful. I wonder if the original mathematicians should start a lawsuit for theft of intelectual property.
  • pizzly 25d ago
    I would expect this for service providers that provide their "free" services but the mathematicians said they paid OpenAI to help generate this result. This is a clear conflict of interest. Similar to inside trading. Or the same lawyer being hired from two opposing sides which is a big no no. There are rules and laws that already deal with this in other industries and I expect that there will have to be regulation developed for cases where there is a conflict between AI customers and AI provider interest.
• soundworlds 25d ago
  I think this is where people will have to let go of the ego of being the "sole author" of a solution for us to move into the next era of human flourishing.
  • samwise99 25d ago
    The future sole owners of half of San Francisco’s mansions thank you for your enlightened stance.
    • soundworlds 25d ago
      The future I'm after involves Open models controlled by the people, not a few SC venture capitalists
• jijji 25d ago
  The lack of reasoning traces in frontier model output is hurting science and progress... thats my take away from reading that, and why open source models are so critical and so needed, because they actually do expose the chain-of-thought reasoning traces recently missing from the frontier models (openAI, anthropic, etc). By encrypting and purposely hiding this important information from public inspection, it makes for a world where people lack the true understanding of how a problem gets solved.
• grog454 25d ago
  > We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. In other words, the "right" people need to solve it: the mathematicians who made it their job and not the people working to push AI models forward? Struggling to understand how a solution to a millennium problem like this isn't a net positive. Presumably Open AI employs mathematicians in these efforts anyway. And I can think of far worse uses of the AI compute resources.
  • xmprt 25d ago
    If there are no incentives for mathematicians to work on and share progress in tough problems because they will get scooped, then they will end up quitting and in net we will see less progress overall.
    • greenowl 25d ago
      Mathematicians can join the club like the rest of us. Time to consider re-training to become a nurse, electrician, auto mechanic, or a plumber.
  • magicalist 25d ago
    > In other words, the "right" people need to solve it: the mathematicians who made it their job and not the people working to push AI models forward? This is not at all what he said? I'm not sure how you got this from anything he wrote, actually.
• gowld 25d ago
  There seems to be a sense wher mathematicians are gamifying math, but are frustrated that AI labs are better at gamifying math. If an AI solves a problem in an unenlightening way, then there's no reason for mathematicians to stop studying it. Pythagoream Theorem has hundreds of different proofs! If an AI solves a problem in an enlightening way, mathematicians should study it and propose extensions.
• qarl 25d ago
  AIs are putting humans out of work. Yes. We already knew this. Are we actually surprised it's happening? I guess we are.
• nadermx 25d ago
  What is this man talking about. You can speak physics into existance now, yet it still has to be proven with math. Until we are walking through worm holes and driving around in spaceships that travel in a warp drive could he even begin to say there is non-renewable. But even then..
• LunicLynx 25d ago
  Why not let AI proof or disproof this Tao - PI - Riemann zeta hypothesis
• xelxebar 25d ago
  There is also a large incentive for OpenAI to fold user conversations into the training process. Proving this happened is unduly hard, and given that professionals are using frontier LLMs for daily work, such training would make it easier for labs to scoop said professionals. I have seen private correspondence between one mathematician working on Navier-Stokes and OpenAI that makes it sound like OpenAI deliberately scooped this Navier-Stokes result. The alleged correspondence also contained veiled threats if said mathematician went public.
• david-gpu 25d ago
  Aren't we in a similar position to what chess went through in the 2000s when Deep Fritz came out, and a desktop PC was able to defeat a reigning World Chess Champion? Did chess players just give up and stop playing? No, they didn't. They used these new chess engines to become better players. Computer programmers and mathematicians will probably go through something analogous. Presumably it is only a matter of time until these frontier models are used to create new interesting conjectures. I don't get Tao's line of reasoning.
  • esteban0x 25d ago
    Perhaps his takes are evidence of just usual human fear to new things. I see he relies quite much on the "community" or "social" aspects of the discussion. I probably have delusional expectation of what a mathematician of his level should be talking about, but I expected from him a pure objective analysis on what to do with this new AI thing , what are its limitations, how it can improve the field and the creation of human knowledge, etc.
• jdoliner 25d ago
  My model of mathematical intelligence for a little while now has been 3 levels: 1. I give you a proof, you tell me if it's correct 2. I give you a theorem, you give me a correct proof 3. I give you nothing, you give me a theorem 1. is largely solved by modern LLMs and they took a big step toward 2. today with the Navier-Stokes proof. But they're definitely not there yet. It's unclear what progress is being made toward 3. for the time being that remains the realm of humans.
• ppsreejith 25d ago
  @Practal's comment is interesting: > Pure mathematics is dead. Long live mathematics. I think all of interesting mathematics is applied mathematics in the end. Powerful AI means that the level at which we can do applied mathematics will be so much higher, though, and many more people will be able to be "mathematicians". The importance of pure mathematics is often argued for by citing examples of important applications that used pure mathematics invented a long time before the application became apparent. We can reverse this argument: by properly developing the mathematics our applications need, we surely will obtain all of interesting pure mathematics. Perhaps the pace of applied mathematics would rise sharply, given cheap intelligence. And this* may end up being the forefront driving progress in mathematics. *Or maybe a split between the human domain and the practical real world. Where the human domain might end up with a variation of a "No machine contributions" policy. Sorta like the recent gcc policy.
• senshan 25d ago
  From "Jokester" by Isaac Asimov 1956: "Early in the history of Multivac, it had become apparent that there was one big bottleneck: the questioning procedure. Multivac could answer the problems of humanity, all the problems, if -- if it were asked meaningful questions. But as knowledge accumulated at an ever-faster rate, it became ever more difficult to locate those meaningful questions." [0] https://web.archive.org/web/20150118004835/http://www.sffaudio.com/podcasts/TheJokesterByIsaacAsimov.pdf https://web.archive.org/web/20150118004835/http://www.sffaud...
  • bityard 25d ago
    I don't see why that should be a problem, as we already know the answer is 42 in any case.
    • aethelraed 25d ago
      There is as yet insufficient Data for a meaningful answer. [1]: https://www.imdb.com/title/tt0708807 https://www.imdb.com/title/tt0708807
      • senshan 25d ago
        ??? http://www.thelastquestion.net/ http://www.thelastquestion.net/
        • deleted 25d ago
          [deleted]
      • TZubiri 25d ago
        The findings of the present study suggest that more funding is necessary, roughly the amount of money necessary for a trip to Burning Man
    • Nition 24d ago
      You may recall though that whole problem with '42' as the answer was the lack of knowledge of the question. The Earth was created as an attempt to provide the question, but was unfortunately demolished to make way for a hyperspace bypass just before the question was resolved.
• sno6 25d ago
  "In a world where the cost of answers is dropping to zero, the value of the question becomes everything" https://www.youtube.com/watch?v=dcolM6W5Odc https://www.youtube.com/watch?v=dcolM6W5Odc
• fwlr 25d ago
  Open math problems, yes; also open source code, art, literature, and everything else as well. AI is a machine for turning commons into tragedies.
• kurtis_reed 25d ago
  Plenty of new open problems will come from applications, and applications are what actually matters. Pure mathematicians are wrapped up in math for the sake of math which is a fun academic game but not something the rest of us should care about.
• pvillano 25d ago
  The way to tame a profit-maximizer is to make the most profitable choice the one that creates the most societal good. I would like to see the Clay Institute give zero recognition for formalizations without human-readable proofs. That would incentivize OpenAI to scram or create something that's actually useful.
  • jfrbfbreudh 25d ago
    It would be trivially easy to convert Lean into English, so I’m not sure what the human-readable criteria gets you. There are also human written proofs that are considered not human-readable by most of the mathematics community (ABC conjecture).
    • pvillano 25d ago
      Human-readable means multiple humans can read and understand it in full. A human-readable proof is more worth more than one that is not, because mathematicians can read the proof and extract value in the form of reusable techniques, additional problems, progress towards related problems, and everything else Tao mentioned. A proof that only a few humans can read is more useful than one that no human can read because the few mathematicians that can read the proof can still extract value in the form of reusable techniques, additional problems, progress towards related problems, and everything else Tao mentioned. That's what the human-readable criteria gets you. Mochizuki's claimed proof of the ABC conjecture is not unintelligable; it has errors. There are no proofs written by humans that are not human-readable, because in order to come out of a human mind, the proof must have fit there originally. The four color theorem states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. It was the first theorem proved with substantial computer assistance. The theorem was proved by showing there could not be a counterexample. The authors made a list of maps where if a minimal counterexample existed, it would be one of these maps. There were 1,834 maps in that list, and each one was checked by computer. You could turn each of those cases into a picture or paragraph, but the resulting artefact would not meet my definition of human-readable. Human-readable does not just mean in English. Humans can only hold a few objects in their short-term memory at once, not hundreds. Though some proofs require significant background knowlege, any proof written by a human will respect the fundemental limits of the human mind. There are no proofs written by humans that are not human-readable, because in order to come out of a human mind, the proof must have fit there originally. I suspect large lean proofs generated by LLMs do not respect the fundemental limits of the human mind. If no human can read and understand them, no one can extract value in the form of reusable techniques, additional problems, progress towards related problems, and everything else Tao mentioned. If LLM proof generators can be made to write proofs with the same value as humans, that would be great! OpenAI would be a celebrated collaborator if they created as much value as a human does.
• sxzygz 25d ago
  Oh man am I totally going to determine the 10^10^10th digit of π and cement my name in the annals of history.
  • bibimsz 25d ago
    it's 7
• meken 25d ago
  I don’t see why it makes a meaningful difference if a human solves a math problem versus AI - it seems like the same amount of understanding will come out in the end. Either the understanding will come from humans arriving at the proof in the former case, or the understanding will come from humans understanding the proof that the AI came up with in the latter.
  • mrbungie 25d ago
    Probably an AI-written Lean proof is very different to how a human would write it, and some may say it's more like mathy neuralese. For sure it works but it is not human-friendly and needs to be transformed into something more readable and digestible to be able to extract insights from it. Not that different from when trying to read an out-of-control vibe coded codebases, or an sloppy AI long email that someone may send you at 9 AM.
    • meken 25d ago
      Tao has a spiel in his recent interview with Dwarkesh where he says that AIs are very good at explaining things - so just have the AI explain the proof in a human-friendly way.
      • mrbungie 25d ago
        For sure, but this was supposedly ~18 million dollars of compute, afaik 100 pages paper / lean proof and only god knows how many bytes of chat interactions + thought traces. Scale matters.
        • meken 25d ago
          I bet it can be decomposed quite nicely though. At the top level, there are probably only like five steps. Dig as deep as you want into any of those steps (i.e. engineering).
          • mrbungie 25d ago
• silver92bullet 25d ago
  I think this highlights one of the fundamental differences between humans and our current AI systems. They can still only try to solve problems in the given well defined parameters they are given (with some exceptions). The human is able in the effort to solve problems to intuit where there may be new interesting problems adjacent to the current problem.
  • akoboldfrying 25d ago
    I don't think we can confidently say, yet, that LLMs can't discover those connections. We just haven't explored them yet, because 99.99% of the prestige is locked up in proving hard results, which also happen to be easier to assess objectively (thanks to automated proof checkers), and so that's where all the effort has thus far been exerted.
    • nullbio 25d ago
      LLMs can discover anything. It is just a matter of creating the right goal function and teaching it the right heuristics. Right now, humans are required because humans know what humans want, and LLMs are not good at predicting what humans want to the point where they can safely and autonomously run off on their own to solve problems we didn't know we had, or to define the problems we have that we're not good at defining ourselves. Once that is cracked, you throw more compute at it and practically every industry will collapse on a long enough horizon - with digital industries going first. Anything that requires physical hardware will require time for the machines to bootstrap, but that'll get there too. Although, there are a few human-centric industries that will survive, for example: prostitution. Maintaining it's edge as the world's oldest and most enduring profession.
      • silver92bullet 25d ago
        Debatably in your scenario the last one will or is already falling with robots that will do that. I think there is a real philosophical question of whether AI will be eventually capable of everything we are. I think the question of what makes us unique as humans needs to be asked. I am inclined to think that there is always something that will separate us as human beings from digital robots. I just believe the language and reasoning used for the last 200 years is no longer sufficient. In 25-50 years I believe we will have a clearer picture. Your view essentially falls into a nihilistic framework if I am understanding it correctly.
• axionbraid 25d ago
  [flagged]
• Alien1Being 25d ago
  Tao's central point seems to be: "In short, the indiscriminate use of powerful solution-extraction tools can achieve the immediate short-term goal of solving problems at hand, but at the cost of sustaining the ecosystem for the next wave of progress, or in understanding the progress already obtained. " I am no mathematician, may have misunderstood his point and would be delighted to receive any corrections.
  • ramraj07 25d ago
    Seems to be it, though Im not particularly concerned about this problem personally. The fact that we all readily accept that modern AI systems can likely solve any math problem that no living genius can, tells me that no task is beyond this system we just need the right harness around it. The exhaustion of meaningful math problems to motivate mathematicians minds seems to be the least of my worries at that point. Inb4 someone suggests that this is not proof that these AIs generalize, I agree thats a popular opinion, but both sides are merely that, with no possible way to prove. I will wallow in my existential dread while you do whatever it is that gives you comfort.
  • kkotak 25d ago
    How is this any different from people in any field that are impacted by AI and lose the utility of their skills and endeavors over the past decades? Are we saying that we're running out of problems to solve because of AI and hence it should be stopped? I am not underestimating the importance of the collective knowledge of the mathematics community and the role of mathematics as the enablers of other sciences, but opposing meaningful progress in that discipline or any for that matter feels counter intuitive. I would rather have the mathematics community start collaborating closely with the this newly evolving and powerful tool to expedite humanity's progress.
    • hn_throwaway_99 25d ago
      Do you see an end state in this? When AI is better than humans at everything (and I used to be very sceptical of that claim but I'm getting less and less by the day), I don't see the Wall-E version of humanity as some sort of utopia, and that's the good outcome.
• kurtis_reed 25d ago
  Tao seems to be stuck in a pure-math-for-the-benefit-of-pure-mathematicians mindset. The rest of us care about applications of math, not math itself.
• kragen 25d ago
  It seems relevant that Terence Tao is the author of the paper that just about convinced everyone that the Navier-Stokes equations blow up in finite time, 12 years ago: http://arxiv.org/abs/1402.0290 http://arxiv.org/abs/1402.0290
• nullbio 25d ago
  There's nothing that AI won't be able to mine and accomplish (aside from being literally human), it's only a matter of hardware and scale at this point. Generalized problem solving is a factor of search efficiency over the problem space. The actual software part is all figured out, the only open questions are how to do things efficiently and what the trade-offs are from a hardware perspective, but if hardware paradigms are unlocked then efficiency becomes a secondary factor for the problems we care about. Why bother making an LLM twice as fast if you can make a chip that can process 100mil TPS, for example. You're already in a ballpark where it can do anything you want, with plenty left to spare. The awkward part about all of this is that we're about to enter an age of extreme enslavement at the hands of the major tech companies if we do not focus on distribution of hardware and research, so that everyone can participate in the abundance and automate their daily lives. If we're beholden to frontier labs because they have hoarded all of the cutting edge hardware and we're left with overpriced scraps, we're collectively screwed. They will ensure a false economy is maintained so they can clutch onto a permanent class hierarchy of haves and have-nots and remain the key global decision makers. Automating hardware manufacturing is irrelevant if the hardware is not being distributed fairly, and is weighted to real scarcity instead of artifical scarcity. Take Louis Vuitton for example. They can mass-produce their products for pennies, but they're artificially scarce and incredibly expensive. Imagine if ALL clothing was the price of LV. Now imagine this applies to every single thing you can purchase (or rather, rent - if some of these "elite" get their way), because they've cooked the economy and swallowed all industry. That's where we are headed if distribution and decentralization is not a priority for the world and we let labs like Anthropic pull off their regulatory capture stunts.
  • xigoi 25d ago
    > it's only a matter of hardware and scale at this point. The AI companies have already bought up the world’s entire supply of hardware. There won’t be any more.
    • unrented7977 24d ago
      Yes, clearly no more hardware will ever be produced. We've sold all hardware, it's over, everyone go home. Spin down the factories, we already sold all hardware we'll ever make.
• randomImmigrant 25d ago
  In short, after after training AI on an extraordinarily amount of human cognitive output, we are now facing the possibility that our ability to train by working on hard problems will be slowly stripped away at least in some domains. It’s like someone offers to build mag lev gym weights. It’s very cool that I can now lift the 500 pound weight with a finger. But what will I do when there’s no power and 500 pounds to lift? Of course, cognition isn’t a single outcome problem like weight lifting. But we build cognition not wholly unlike how we build muscle: one needs resistance. Otherwise I’m not at all confident we “learn” in any depth.
• singularity2001 25d ago
  Strong disagree. They are of course infinitely renewable. Just work harder, Tao ;)
• devilfileprong 25d ago
  [dead]
• fooker 25d ago
  Other mathematicians for the last ten years : Open math problems being non renewably mined by Terrence Tao. Jokes aside, this seems like a pretty weird take. What's stopping mathematicians to make this renewable? Why not spend some time and effort (presumably using AI) to pose new open problems that are fundamental in nature? As a field, math could start crediting the person who comes up with a great question, rather than the AI brute forcing a LEAN proof.
• thomascountz 25d ago
  There's an analogous (albeit, far less existential) problem in software development. If the answer to, "what should we build next?" is simply, "yes" (so to speak), then the real value is in the discernment of "what is most valuable, useful, sustainable, and/or meaningful thing to build next".
• ltononro 25d ago
  Will the next generation of mathematicians be the ones to ask questions instead of solving them? I think that is what the math/physics research is moving towards
• 123-2dsh 25d ago
  This is such a funny thread. First, a politely worded letter expressing concern about scooping while carefully avoiding to mention the term. Then an AI bot draws a false Ramanujan analogy, is corrected several times but keeps insisting. At the end a meek comment that Tao helped in opening Pandora's box, without engagement or likes. Modern academics have been conditioned to feel powerless and obedient. The proper way would be to ignore all AI proofs and not grant them access to journals, because OpenAI admitted themselves that plagiarism cannot be ruled out.
• mathaccount101 25d ago
  After 20 years of prioritizing problem solving to the detriment of other mathematical skills, this problem solver point of view is about how to keep the control over the domain. Now that problem solving proved to be easy, mathematics will become even more interesting.
• redwood 24d ago
  I hate to be the one to point this out but how have we gone to the point where one of the world's Premier mathematics thought leaders is communicating through a medium that requires clunkily reading and combining multiple distinct sections and 'read more'links just to get through the thought
• killerstorm 24d ago
  Hmm, can't we just keep a better track of who comes up with some idea/concept/problem, etc, not just "who published a proof"? It seems like new age requires a new form of publication instead of sticking to 17th century concept of a "paper".
• Nevermark 24d ago
  In the comments: > @tao curious to know what makes LLM fundamentally different compared to (other) automatic theorem provers? It highlighted that "automatic" is a spectrum. And the norm is shifting toward "fully" (even if the process is chaotic).
• nater5000 24d ago
  I hear what he's saying, and I'm not saying he's wrong (in essence), but I think Tao (like a lot of other people) are going to have to get with the program a bit. AI is going to radically change a lot of things. It's going to radically change mathematics. It's going to radically change the way people think about mathematics, study mathematics, value mathematics, etc. There's no stopping that. What Tao needs to be contemplating is what that new world for mathematics looks like, cause trying to preserve what we have, now, is effectively impossible at this point.
  • Mond_ 24d ago
    Tao is so incredibly ahead of the curve in this regard that you trying to accuse him of not "going with the program" is a bit silly. He's not an AI Luddite by any means.
• diedyesterday 24d ago
  On the virtue of scarcity, being mortal, being NOT omniscient, NOT omnipotent, being Finite, etc. (thus arising the need to optimize, etc.): [Fig Tree] "By end of the story Gilgamesh is human; He is Us; We see the Deep; That's our gift as humans; We fight to understand something no god could ever could (emergence and richness from scarcity); The gods don't need to fear death so they don't have to live an impassionate life; It means nothing to them to run out of time; "Seeing the deep" is the apex of human potential, not a transgression into godhood; It's something that only humans can do."
• torginus 24d ago
  By the way, am I ignorant of modern mathematics? I love the thrill of a good puzzle, but I'd say a lot of solving these kinds of intellectual challenges is mostly for the mental thrill, rather than advancing humanity. It's self-serving. That's how I view modern math. There's the occassional discovery, like Linear Algebra, or the Fourier Transform which has basically allowed math to improve civilization to such a degree, that they deserve to be counted among the most important works of civilization. Yet the best these weird math theories usually provide is proving something is fundamentally hard to compute, or distributed in some peculiar way, or maybe knock down some of those aforementioned problems into easier tiers. This all ends up practically in cryptography. Hashes, symmetric asymmetric crypto, zero knowledge proofs etc. etc. These are well and useful, but not that useful and the new ones often end up functionally identical to the old, from an utilitarian point of view.