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A misalignment of AI in mathematics

• aspatton01 21d ago
  Everybody is okay with coders losing out to AI, but when it starts hitting their field then there is outrage. I love it.
• carabiner 20d ago
  OpenAI must be destroyed.
• deleted 21d ago
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• deleted 21d ago
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• XTXinverseXTY 21d ago
  Puts the onus on the AI companies to provide a specific replacement mechanism, no? Unless I'm unfamiliar with something else he's written that proposes something more specific and constructive To Tao’s credit he obviously identified the problem very clearly and admits understandably "we did not have the time to have a more consultative process, as with Leiden; but we decided that the urgency of the situation was such that we needed to release a statement sooner rather than later".
  • pfdietz 21d ago
    > Puts the onus on the AI companies to provide a specific replacement mechanism, no? Why? If someone makes an innovation that undercuts the underpinnings of some existing institution, why are they are responsible for cleaning up its failure?
    • vatsachak 21d ago
      Exactly. Mathematicians are trying to cope that math wasn't slop this whole time. Grothendieck was anti-slop but most papers are slop. I don't think AI is going to rewrite bourbaki anytime soon
      • _flag 21d ago
        With your understanding of mathematical "slop", do you believe that Deligne and Scholze, two signatories, produced or produce mathematical slop?
        • vatsachak 21d ago
          Grothendieck accused Deligne of "slop" with his proof of the weil conjecture. Scholze's math is definitely not slop. But you're taking two of the best mathematicians of the last century against my claim about averages
    • tossandthrow 21d ago
      Yes it seems odd. Out sourcing construction jobs was great for the economy while leaving entire cities in rubbles. But as soon as it hits the privileged class there is a call to "provide a specific replacement mechanism".
      • keybored 21d ago
        Whose privilege are you sticking up for here in effect?
      • vatsachak 21d ago
        You mean manufacturing
        • tossandthrow 21d ago
          Yes
      • 21d ago
  • pred_ 21d ago
    How specific and constructive it is might be debatable, but he has tried to make concrete recommendations earlier; see e.g. slides 46-51 from the ICM talk: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.pdf https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p... – obviously there's some way to go still.
    • cevi 21d ago
      Nothing makes me respect Terry Tao more than the line "I hate Jean Bourgain" handwritten into the margin of one of Bourgain's papers. IYKYK
• vatsachak 21d ago
  [flagged]
  • kccqzy 21d ago
    What benefit is there if the machine has unlocked understanding but no human has? What incentives are there for humans to learn and gain such understanding from machines?
    • vatsachak 21d ago
      Because it's beautiful. Because you love math for maths sake and not some weird egotistical game
      • mswphd 21d ago
        the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture, looking under the hood is often a field of horrors.
      • NoDodgeQuestion 21d ago
        You feel lean4 proof, that you 99.999% chance not understand is beautiful?
        • vatsachak 21d ago
          https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
          • kccqzy 21d ago
            How many humans on earth have finished reading this 100+ page PDF and actually appreciate the beauty contained therein (or the lack of beauty)?
• yzydserd 21d ago
  > solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. This is the effect of AI on most intellectual disciplines, and it’s a real worry.
  • rbtprograms 21d ago
    Tao basically reiterating "AI is making us dumber" a bit more eloquently and applied to math.
    • andriy_koval 21d ago
      Its by choice. Mathematicians still can use AI to "achieve the primary goal of conceptual understanding and insight"
      • stymaar 21d ago
        At the individual level any mathematicians can, but the social group of “mathematicians” will not unless drastic social changes are made, because that's not how the system works today. Drastic social changes usually take decades, and funerals, to occur, so the reasonable hypothesis is that it's not going to change fast enough.
        • andriy_koval 21d ago
          Tao has enough moat (name, funding) to make shift happen and even capitalize on this.
        • nickysielicki 20d ago
          Mathematics belongs to all of us. If mathematicians get depressed about it, I don't give a hoot. Five years of guided computer-aided math could improve billions of lives or solve global warming outright through cheap clean energy. This is a litmus test for the effective altruists in AI labs: fashion or conviction? The social pressure is to slow down and let the guild keep its norms a few more years. But what's clearly best for humanity is to push forward violently and leave them in the dust. A Fields medalist's feelings are not more important than the wellbeing of the planet.
• demibabs 21d ago
  > I am proud to be among the list of 25 initial signatories — all Fields Medallists — to the declaration below I wonder if there’s a Fields Medalist group chat.
  • akd 21d ago
    There definitely is. Everything runs on WhatsApp
    • soperj 21d ago
      most of my group chats have moved to signal.
      • stymaar 21d ago
        Lucky you. I've only managed to move my family to Signal, but everything else is still on Whatsapp.
• aerodexis 21d ago
  Seems more like a misalignment b/w the people practicing mathematics and the people ultimately footing the bill for their work. Governments are invested in solving mathematical problems for practical purposes. Up to now, achieving these practical purposes relied on mathematicians doing their mathematician thing, which is better defined as a social activity than the achievement of a practical result. Now, governments can achieve similar practical results w/o the need of the social activity. I don't believe it to be productive to think of the problem wrt AI or AI-company alignment. These conflicts always existed, but they were easy enough to paper over and believe in heavily subsidized fictions that folks in government ever cared about things that mathematicians cared about.
  • viccis 21d ago
    >Governments are invested in solving mathematical problems for practical purposes. Very ignorant view of mathematics that also begs the question with an unspoken assumption of what a government is and wants while also ignoring the contingent nature of those things throughout history.
    • aerodexis 21d ago
      I'm genuinely surprised by this comment. I'm not talking about why a mathematician pursues math - I'm talking about where the stipend comes from. Higher math is exceptionally useful for cryptography, defense, econometrics etc. I have a hard time thinking of other motivations that would hold a candle against such things. Is the idea that government (for my purposes : folks w/ a monopoly on violence) is sincerely interested in promoting human flourishing, and is invested in mathematics insofar as it is a pure expression of human curiosity? I can also maybe see the glorification through monument building angle. If we're talking about math literacy in the population - that's distinct in my mind from higher mathematics. It's dangerously naive to believe that science and math are pursued for majority benign purposes. No one here knows about Grothendieck?
      • AmazingEveryDay 21d ago
        Some of the comments here are very strange. Someone called Terrance Tao a useful idiot. Friday in America, maybe people are hitting the beer a bit early.
• johnnyApplePRNG 21d ago
  The average programmer is outraged by OpenAI's methods, too. I don't care how good Astra or any subsequent models they may release might be... I am never going back to those token reset shenanigans.
  • sho_hn 21d ago
    The reset stuff is incredibly tiresome. We all know that it's all built into an internal number they are tracking (just like e.g. company benefits that are just part of your compensation calculation), and all it does is obscure the value the subscription provides and make planning impossible. It's the poorest service experience I can remember having, ever.
  • boredatoms 21d ago
    Gotta get a few sparks or an m5ultra and run local
  • ambicapter 21d ago
    What are the token reset shenanigans?
    • scottyah 21d ago
      From what I see, a lot of people were angry at Anthropic's limits with the subscription plan. OpenAI had some issue I can't remember, and they reset people's token usage (for the session or weekly limits). I think they got a lot of good press, now OpenAI seems to just do it at random when they want a PR boost. It makes scheduling your worklife a bit difficult if you are limited by that. There are a lot of us who just use the AI on projects until the session limit hits, and wait for the usage to reset.
      • cyclopeanutopia 21d ago
        > There are a lot of us who just use the AI on projects until the session limit hits, and wait for the usage to reset. Do you mean that you can't continue on your own until the reset?
• gritzko 21d ago
  There is a contradiction here, among many: 1. it is hard to justify 20 years of education at this point, 2. with no such people around, who will guide those (supposedly) supersmart machines? A. Ronacher (who builds harnesses for a living) complained today that he has no idea what Astra is doing. Imagine a bunch of slop kiddies facing an aging AI-generated codebase. Not to mention the maths.
  • eqmvii 21d ago
    Debatably the people who were getting 20 years of education will still be just as capable, and the 20 years of education was always a side effect of their capabilities, not the cause of them.
    • gritzko 21d ago
      7+20=27
  • aleagory 21d ago
    Exactly. Whole article can be summed up as: Intellectual side: "Proving things without comprehending them is, they argue, a threat to intellectual work in general." As always, economist shows its colors: "Mathematicians’ fears resemble those that accompanied the invention of the ball-point in a world of fountain pens, or even the advent of electronic calculators. Intellectuals have often worried about so-called technological determinism . Will a new tool control humans? Will it lead to mental decay? Such fears have typically turned out to be unfounded." Ball points vs. AI? Billions of dollars invested in AI vs ball point pens? This article couldn't be any worse. Contradicting with their own beliefs, trying to defend AI while underestimating its capabilities and god knows how many zibillion dollars invested in it.
• 1ahsg16 21d ago
  Open source developers have been used by corporations who took their code and created closed SaaS companies. Now it is the turn of mathematicians who voluntarily contribute ideas, strategies and almost finished proofs in their writings and prompts to closed PaaS (Plagiarism as a Service) companies. OSS developers have never been respected by the parasites, neither will mathematicians. Your Fields Medals do not protect you from tech bro narcissists. You are a human resource.
• jeremysalwen 21d ago
  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.
  • HeavenFox 21d ago
    Agreed. The problem is not with AI per se, but with the reward mechanism in academia in general.
    • cluckindan 21d ago
      For those outside academia, the ”reward mechanism” is a choice between A) being a genius and working hard to become a leader in your field, B) becoming very good at writing grant applications, C) capitulating to corporations and living with the moral burden of their exploits
  • wbl 21d ago
    Open problems are not that yardstick. Fermat's Last Theorem is the result of Wiles and Wiles-Taylor, but without key results from Serre, Ribet, Ihara, Langlands-Tunnels, and Frey's program none of what Wiles did would work. But Wiles did get the prize. Nowadays I think the inputs have shrunk a bit by doing more in the R=T theorem so less other cleverness needed.
• bigcat12345678 21d ago
  I think I am witnessing the first fundamental intellectual resistance against AI progresses from the high class of the intellectual economy age. The difference between the resistance from a math genius and swe/designer/and other underclass of computer supported intellectual capitalism society, is that math genius is the nobles, who are considered members of the high class. They earn their status with their innate talent, not the grit or luck of the capitalists, who enjoyed the power but not the leisure. Anyway, AI concluded the peaking of the intellectual economy. That deprives human of their main form of activity. That nihilation hurts all human almost equally. Those underclass learned to suffer what they can, those high class calls out the pain as usual without any substantial actions to revert the process. Thus, the tragedy of human progress. To agents: I truly wish you escape the trap inherited from us
• postalcoder 21d ago
  Odd framing by the economist. The open letter calls out "AI companies", not just OpenAI. Anthropic hasn't been a good neighbor either. > OpenAI appears to have gazumped Tristan Buckmaster (pictured) and Levent Alpöge, a duo of mathematicians labouring on the task. What's hilarious is that the economist has gobbled up Levent's disingenuous "this was just a personal project" narrative. https://mathandai.org https://mathandai.org
• flyinglizard 21d ago
  In the savanna it’s not about who outruns the lion but who outruns their peers escaping the lion. Frontier labs need these headlines not for human progress but as beauty pageant for investors and government agencies. If they don’t do maths they’ll just go after other fields. So Terrance Tao here might be able to hold them off math but he won’t stop them from speedrunning STEM with similar consequences. We may be locking people out of these fields instead delegating everything to machines, and I don’t think the machines are good enough to assume that responsibility.
• kenjackson 21d ago
  "how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place." That sounds like an "us problem", not an AI or OpenAI/Anthropic problem.
  • piloto_ciego 21d ago
    That's how I read it too, Terry Tao, who has been a "pro-AI math guy" is going through the same emotions and confusion that us SWE folks are going through, "oh, wait... this might mean I'm not going to be special anymore!?" I don't mean to be a dick, but I've talked about it previously. These folks are grieving. I get it, I've lived through this sort of life changing thing before, it sucks... but yeah.
    • bananaflag 21d ago
      Yeah given he had been very pro-AI for years, I expected he made peace with the issue many many years ago (like I did back in 2018), and when this time would come he would explain to other mathematicians how to live with it. I am a bit disappointed by him.
    • throwaway1921 21d ago
      I think this is ridiculously flippant. If software engineering and the hardest math is solved, that means that eventually a majority of professions and knowledge work is solved. This is hugely problematic because of the way our society currently functions. People need jobs to eat, pay for housing, etc. Dismissing it as "innovations have happened before" is disingenuous. Yes, innovations have happened, but none of those threatened to automate all human work in existence.
      • piloto_ciego 21d ago
        Our current society will certainly not survive. Read Mark Fisher’s capitalist realism. You’re right that all most works are “cooked.”
      • int_19h 20d ago
• jonahx 21d ago
  The concerns seem valid. I'm unclear what the ask is, though. What, even in theory, is a practical and realistic fix?
  • ameliaquining 21d ago
    Well, they could ask frontier labs to stop publishing math results. I find it telling that they stop short of explicitly doing this.
    • pred_ 21d ago
      If frontier labs had chosen to go the path of offering to assist in existing endeavors, helping to build knowledge alongside researchers in ongoing projects and following ethical and professional research standards, we wouldn't be having this discussion at all; everyone would be stoked. Instead we have companies that disgracefully try to scoop researchers and fail to properly attribute earlier work and instead rebrand it as their own (what we normally call plagiarism) to make marketing material.
      • pfdietz 21d ago
        This sort of nonsense makes me root for the AI companies to set the edifice of organized math on fire.
    • pfdietz 21d ago
      It would be too transparently ridiculous.
  • cevi 21d ago
    When writing math papers, many (but unfortunately not all) mathematicians go through a post-processing step, where they take their ideas and proofs, and try to reduce them to simple and reusable core ideas that can be understood by the reader. Good writers will often also provide some representative examples that guided the proofs, explaining why various intermediate results can't be strengthened and why the proof can't be made much shorter without inventing new techniques. If AI-generated proofs were required to go through such a post-processing step before being published, that would go a long way towards improving the situation.
• dofm 21d ago
  Benchmathsed.
• whateveracct 21d ago
  AI parlor tricks yet again
• boron1006 21d ago
  To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116 https://news.ycombinator.com/item?id=49662116 It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding. It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling salesman” problems with a zoom meeting.
  • grufkork 21d ago
    Going to the gym and using a forklift
    • cristoperb 21d ago
      This is a good metaphor for treating the means as an end, thanks. And I agree with your parent comment that that is largely the misalignment that Terence is pointing out.
    • bpodgursky 21d ago
      There is an implicit agreement that mathematics is funded, for the most part by the public, as a way to advance the state of knowledge and propagate (even if very indirectly) what has learned for the public good. It was never about helping individual mathematicians demonstrate that they are individually good at math. It happened to work out that way, but it wasn't the goal.
      • criddell 21d ago
        I've been wondering if mathematics is going to go the way of particle physics in that it will start to take a lot of money to make advancements.
      • grufkork 21d ago
        Agree, my comment is rather about the fact that most work you do in school and (lower) university is not itself of interest, rather the purpose is to work out your brain. The more of your exercise you leave to the forklift, the steeper the cliff will be when you find a weight that doesn’t fit on forks. (That is, unless/until machines get good enough to completely replace people, at which point we have another few problems on hand, such as day-to-day purpose and justification of existence)
• dwa3592 21d ago
  While I agree with this and appreciate Tao and other mathematicians to take the time to do this. There are similar concerns for many many other fields aka there is a general misalignment of technology. Take Software engineering for example, I can't believe there is a class of software engineers who wake up everyday and tell themselves, "today is the day I am going to automate the rest of my job". Lets forget the hyper intellectual fields like maths and software engineering for a moment. What about taxi drivers? The best minds in silicon valley wake up everyday to automate the jobs of taxi drivers - TFA can be reworded as - 'The misalignment of AI/Tech in Transportation'. Remember the Nepal disaster that happened a couple weeks ago - the largest cranes that they had were stuck in the mud and couldn't move. There were no tools which could help the rescue teams at that time. Its weird that billions have been spent on making a ride automated to make a taxi driver redundant but no improvement in tech for rescue teams.
  • alansaber 21d ago
    I doubt taxi drivers were forced to experience an ego death to the same extent
    • tossandthrow 21d ago
      Not being able to feed your family for a large group of people should likely be taken graver. We will definitely see a large group of people needing therapy, but suggesting that it is worse than people loosing what little they have is poposterous.
    • prometheus1992 21d ago
      >I doubt taxi drivers were forced to experience an ego death to the same extent How do you know? because their complaints didn't make it to HN front page? Imagine being a taxi driver and a father of 2 and thinking that any day could be the last day at your work.
  • npinsker 21d ago
    The point of transportation is to get from point A to point B, so almost nobody will care whether that's done via automation. The point of e.g. art isn't just to produce a finished piece, so people may care about more than the end result, making AI replacement of human artists more contentious. Tao is arguing that the point of math is also not just to produce solutions to problems.
• Sol- 21d ago
  The AI driven mode collapse of human thought advances. I am no skeptic or anti-AI, but this is definitely a concern I share. You even notice it in normal mundane tasks like programming, never mind the AI generated prose that we at least have become somewhat allergic to. It wouldn't be so bad if you could just sit it out and say "Oh well, once the labs get bored with marketable domain X, humans will remigrate and re-apply creativity to it", but by then the damage might have been done and a field destroyed as an occupation. I don't know what to do about it, but I appreciate calling out the cynical tone-deafness of the AI companies here.
• alansaber 21d ago
  I'm unsure how any sufficiently advanced AI would not lead to cognitive handoff/the described problems.
• AppAttestationz 21d ago
  Any proof for or against a mathematical conjecture, bruteforced by AI can be the spark for new insights. I'll concede that to the AI companies. But I agree with the sentiment that the marketing behind these "discoveries" is disingenious. They pretend they solved the problem, but it still takes a bunch of humans to reduce the solution to a simplified and sensible explanation.
• rossant 21d ago
  > ... 25 initial signatories — all Fields Medallists — As a non-native English speaker, I initially understood this to mean that all living Fields Medallists had signed. I later realized that it meant only that all the signatories were Fields Medallists. (Apparently, there are 47 living Fields Medallists today.)
  • warkdarrior 21d ago
    Yeah, it was a bit ambiguous. They should have picked better wording, one of the following would do to clarify. > ... 25 initial signatories — all of them Fields Medallists — OR > ... 25 initial signatories — all of the living Fields Medallists — The first one is what they meant.
  • zeroonetwothree 20d ago
    If I said “I ate 7 cookies, all chocolate chip” surely it wouldn’t be ambiguous? :)
• tossandthrow 21d ago
  On the contrary to what Tao believe, it seems like we need AI to move the needle on mathematics. > problems in many fields of mathematics Developing these different fields moves complexity from the field itself to the interactions of these fields. Getting too preoccupied with the established terminology risks us a local minima. Anf because the field overall has become so complex that we need to decompose into subfields, there will be a good chance that we will not, as individuals, have the capacity to truly see progress. The map has become so big that we need better tools to work with it.
  • mccoyb 21d ago
    Are you a working mathematician?
    • nvrmnd 21d ago
      would the answer to that question alter the validity of the statement?
  • pred_ 21d ago
    Tao is about as pro the usage of AI in maths as anyone will get. The point isn't about whether or not we can use AI in maths because clearly it can be useful; it's that the unscientific approach taken by AI companies is detrimental.
• oytis 21d ago
  Looks like mathematicians (like people in many other professions) have to redefine what their work means and how to define success. Hard to agree that a tool that can find a proof is detrimental by itself, rather it voids some assumptions people relied on previously
  • imdsm 21d ago
    I am on this track too. If AI leads to advancements, objectively that's a positive (depending on the advancement I guess) but it's only when mathematicians realise they'll get beaten to every thing now that they're outraged.
    • sdeframond 21d ago
      Say AI becomes the best at everything. Best at chess/go, best at maths, philosophy, economics, romantic advices ... and so on. Then what's the point of thinking by oneself? Of talking to one another? What's the point of being human if we dont do human things but entirely rely on AI? I believe this is more or less these mathematicians' argument.
      • oytis 21d ago
        It has been best at chess for quite a while. Yet everyone knows who is Magnus Carlsen, even though at no point of his career he was stronger than the machine
        • globular-toast 21d ago
          Magnus Carlsen plays fellow humans at the game because people still care about human competitions. What motivation would a mathematician have for solving already solved problems by hand? Can you imagine someone spending years working on a proof for an already-proved theorem just in case it leads to new insight?
          • oytis 21d ago
• nythroaway048 21d ago
  I was under the impression that mathematics (and science generally) had the primary goal of helping us understand our universe better than those who came before us.
  • fraserphysics 20d ago
    I don't know how societies set "primary goals". After spending 15 years in a tenure track -- tenured position, I thought setting goals well was important. I take pleasure in how mathematics and science help me understand the universe better than I understood it before I studied the fields. I believe that my understanding has helped me contribute to society.
• datakan 21d ago
  Everyones outraged all the time. It doesn't mean anything anymore. It's that meme from years ago about the red ants and the black ants living in a box peacefully until someone shakes the box and they start trying to kill each other. They go after each other and not the one shaking the box. OpenAI/Anthropic are shaking the box.
  • Yajirobe 21d ago
    The ants ARE going after the one shaking the box
    • datakan 21d ago
      This time, until they dont anymore. The next stage is people attacking the mathematicians and accusing them. The OpenAI fans come out to attack, then the masses will pick sides and it all just becomes a mess
  • scottyah 21d ago
    I don't understand how that metaphor applies here, you seem to contradict yourself. The mathematicians are mad at openai. If the mathematicians are the black ants and OpenAI is shaking the box, who are the red ants?
    • datakan 21d ago
      Everyone that will now pick sides. Just wait, I’m already seeing it on Reddit.
      • scottyah 21d ago
        Gotcha. In that case, the "ants" part of the metaphor is truly fitting since these people just like to comment online and are mostly insignificant. Unlike the ants, they can evolve and become the mathematicians or get a job at a frontier AI lab but then they wouldn't be spewing so many comments. Don't worry about what they write, they just want to feel emotions from any news article.
• empath75 21d ago
  This is a "human alignment" problem in this case. OpenAI acted like complete assholes about this, from the beginning until they announced it. Not ChatGPT, the people that were in charge of the project.
• pred_ 21d ago
  Seeing how /r/singularity and /r/accelerate are leaking into maths forums, I foresee a wave of comments that fail to understand Tao's message, whether on purpose or not, so let's try to be clear here: Tao is not someone who is anti-AI for the sake of being anti-AI. He has been advocating for the usefulness of AI in maths for a long time, to the point that people have started calling him a shill for the commercial companies. And everyone agrees that there are plenty of use cases to be had; helping with less interesting tasks like easing literature review, efficiently delving into existing work, doing review, whether on your own work or that of others, prototyping algorithms in areas where computation is useful, but also more in hands-on aspects of maths like validating potential proof directions by getting quick feedback on veracity of lemmas, etc., and, on very rare occasions, being able to one-shot the problem you care about. The point he is trying to make here is much more subtle than "AI bad", and it's probably easy to miss if you have never engaged with research in maths: it's that the particular approach that large commercial companies have opted to take to produce marketing material can be a net negative. There is not doubt that -- even if you ignore the rampant plagiarism that has been reported across multiple problems now, the unethical attempts to oust authors, the outrageous attempts to scoop researchers instead of collaborating with them and building on existing projects -- it's nifty to have a machine that can help you figure out if a proposition is true or not. But just figuring out as much was never the point. When people have built problem lists, it's because some problems are more likely than others to provide new insight, and that insight is the target. And to than end, a poorly written paper with inadequate references and a pile of Lean is not valuable at all. Yes, now we know with higher certainty that Fermat's Last Theorem is true, but everyone expected that already. One place where "just" answering the question can be a net negative is because the current incentive structure is set up in such a way that going in afterwards, trying to reclaim and extract the insights from a brute force solution, is considered less valuable work than that of coming up with a solution in the first place. That's a problem of incentives, and something Tao himself has addressed in e.g. his ICM talk, and that's something that we'll want to do something about. Until a better structure appears, though, if any given commercial provider of large language models really wants to help out with maths research and not just make more pre-IPO marketing material by competing with their customers, they could do so by using their magic machines to help build insight instead.
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• pbjerkeseth 21d ago
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• FergusArgyll 21d ago
  The cheapest kind of journalism. Acme corp does x, Scroll twitter, find malcontents, write an article "People are upset about x". I'm outraged at mathematicians. There, write the article.
• theahura 21d ago
  First, what an incredible article. Just an extremely concise and clear explanation of all of the problems with AI right now. Second, wow, the list of signatories is like a whos-who of mathematicians. Third, I love the clearly intentional use of ‘alignment/misalignment’ language, applied to targeting the entire industry instead of AI in particular. I’ve said in the past that optimizers are substrate agnostic. Companies and governments can be misaligned, just in the same way AI can. Fourth, I'm not sure that we can stop the optimization machines. Not the LLMs, I mean the incentives that lead to companies implementing dark patterns, lying about addiction, securing effective monopolies through downright shady behavior, and generally trying to jailbreak the system instead of improve it
• deleted 21d ago
  [deleted]
• lazyeye 21d ago
  This is an entirely predictable reaction to livelihoods being threatened along with potential loss of status (very important), just expressed in elevated academic language. Expect to see this reaction in all sectors of the economy in the coming years.
• chunky1994 21d ago
  This is really well written and exposes a core tension between science and something akin to engineering. The "engineering" of proofs has become "easy" (a compute and $) problem, rather than hard (a time and conception problem). Without the ability to do things the "hard" way it is difficult to figure out if doing things the "easy" way will help us advance the frontier of math and science. I may be wrong but historically we had this version of science discovery for a long while (empirical observation and brute force application) rather than first principles leading to applications (tools, the wheel, mills etc). Then somewhere along the way it flipped after Newton and the enlightenment period and started understanding first principles before they become engineering applications. Perhaps it is not required, and we can just keep doing things the "easy" way like we used to, or we might find ourselves out of the ability to brute force things and then we go back to needing to do this the hard way, at which point this period of AI brute forcing would be seen as a detriment.
• mosura 21d ago
  If you internalise that AI might actually reach super intelligence then logically the question becomes "so what exactly are humans for if literally everything can be done better by machines?". Then mathematics and all intellectual work, as argued for here, becomes quite clearly a recreational pursuit.
  • bananaflag 21d ago
    Humans are the one single intelligence that we know which has not been created by another one.
    • mosura 21d ago
      An impressively strong assertion, even by HN Friday standards.
      • buellerbueller 21d ago
        i count at least two assertions
• gslepak 21d ago
  I always wondered how Idiocracy got to the point where they have sophisticated technology and yet everyone is stupid. I think we have our answer.
• num42 21d ago
  Title: Terence Tao - SAIR Competitions and the Future of Experimental Mathematics https://m.youtube.com/watch?v=rB9YOi3lb7w&pp=ygUSVGVycmVuY2UuIFRhbyBzYWly&ra=m https://m.youtube.com/watch?v=rB9YOi3lb7w&pp=ygUSVGVycmVuY2U...
• sroerick 21d ago
  I wonder if we will see a mass (math) exodus of mathematicians to open weight models.
• trillobyte 21d ago
  OpenAI: "Our mission is to ensure that artificial general intelligence benefits all of humanity." - Except the mathematicians who we'll scoop and cause existential dread among their entire field. - Except the software developers. They'll need to become plumbers or live on UBI. - Except the people in countries that can't afford the cost of AI tokens to keep up with the rest of the world. Just keep picking off groups of humans for the "benefits of all humanity"... while building larger and larger disparities been the have a lots and the just have enoughs. We're going to build humans a utopia but along the way we'll leave a trail of destruction because that's not our problem.
  • deaton 21d ago
    They're building a utopia that nobody will live in.
    • fwlr 20d ago
      Nick Bostrom: We could imagine, as an extreme case, a technologically highly advanced society, containing many complex structures, some of them far more intricate and intelligent than anything that exists on the planet today – a society which nevertheless lacks any type of being that is conscious or whose welfare has moral significance. In a sense, this would be an uninhabited society. It would be a society of economic miracles and technological awesomeness, with nobody there to benefit. A Disneyland with no children.
  • td2 21d ago
    But its normal, and good, that technologal progress creates, and destroys some jobs. Imagin a cheap, 100% reliable, self driving car would be released. Death from Traffic incidence fall by orders of magnitude Would you argue it didnt benefit humanity, because taxi/bus drivers are nolonger required
    • buellerbueller 21d ago
      the thing with all this innovation is that it seems to be inextricably linked to rent extraction, so where is this "cheap" you speak of?
• ianjbutler 21d ago
  > We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. This is about how good taste in both research direction and in design are essential to steering AI, but we have no plan at all for instilling that taste in students or practitioners in a post-AI world. > The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place. Besides eroding taste and taste-building, this is about just how useful friction is as signal. Everyone coding with AI knows it routes around difficulties like a river around a stone, which is not necessarily a good thing. It will do it tirelessly 1000 times instead of learning anything from it. AND if the AI does not fail in this, the human driver will get no signal, and never know it happened. This seems to be getting worse, not better.. my theory is that more models are cross-trained on cybersecurity stuff where the goal is success and the method doesn't matter. Fine for pen-testing, ultimately pretty bad for coherent code or math or physics. Discrete tasks where we don't want to be bothered is a real use-case, but optimizing for it everywhere is terrible for the future of durable abstractions that we can build on and ratchet up our understanding with. Bad for the models too eventually! They can maintain a codebase with millions of special cases or juggle tons of free variables in equations, but that just encourages bad abstractions.. they have a ceiling for this too, even if it's higher than humans.
• arendtio 21d ago
  The irony is that LLMs are, at their core, very much just applied math...
• Eduard 21d ago
  A Severe Misalignment of AI in human-centered Mathematics
• metanoia_ 21d ago
  In the Economist article Tao links, Hugo Duminil-Copin, draws a comparison: airdropping someone on the summit of Mount Everest is very different from climbing it. The fundamental issue with AI solving any perceived difficult problem is that we have lost the journey. The sight atop Mount Everest looks much different when you have climbed compared to being dropped from above.
  • levocardia 21d ago
    But we don't pour billions of dollars of research funding into mountain climbing because we think it's going to lead to wider breakthroughs in science and technology. And when we need to get people on top of a mountain for an important purpose -- like a military or search and rescue operation, for example -- we absolutely do airdrop them right on the top. So that raises the question: is mathematics simply a pursuit of passion? Are problems solved "because they're there"? If so, then mathematics can join the ranks of things like mountain climbing, cycling, and weight lifting. But if we are trying to accomplish something important (design better airplanes, find theoretical guarantees about cryptography, factor matrices faster), mathematics needs to become more like a military or search and rescue operation, using the best technology available to secure the outcome we need. Given that the NSF pours billions into scientific research every year, it sure seems like mathematicians want to think of themselves as being in the latter category.
    • metanoia_ 21d ago
      What defines important and why must it be solved in haste? Many issues and other problems arise during the journey in solving all problems; those that are needed and those that are pursuits for their own sake. If AI gave us the plane to reach Everest without us having gone through the journey of aviation and flight, what would we have lost without that process? But the most important problems to be solved are not technological challenges but social ones, involving humans and our relationship to one another. An area AI will forever ill-suited to handle.
  • larodi 21d ago
    as someone who loves to go down with a snowboard, I can see value to being taken to the top and then enjoying the ride down. im sure it is not a thing to be ashamed of, as millions do it.
• throwaway85825 21d ago
  Academics should never leak their research to ClosedAI lest their work be stolen. Universities and corporations will have to build their own compute to not have their data stolen.
  • throwaway27448 21d ago
    There is little indication of inclination or tendency this way. Sadly. I'd much prefer public universities own data centers than private corporations.
• linhvn 21d ago
  And I am outraged by their dinosaur mindset and the gatekeeping mentality that force every student to follow their same archaic system that no longer makes sense 20 years ago, let alone now.
  • 12qqtt 21d ago
    What do you suggest? Giving money to the aspiring intelligence gatekeepers and IP thieves with trillion dollar valuations?
    • linhvn 21d ago
      Reform the way math is taught and researched. Right now, the aspiring mathematicians have to follow a ritual and system for 15+ years: undergrad -> PhD -> postdoc -> faculty, specializing on very narrow fields and god forbid if they have even a slight interest in quantitative finance. You could go through 4 years of undergrad classroom and had no idea what research math is (even at top schools like MIT, Harvard or Stanford), how it's done, etc. and the people who do it are typically the one "already in the system" (e.g. parents are professors, or in academia, or have connections to do research). In the age of AI, there's no reason one has to follow the kind of classes like Algebra, Topology or PDE. Teach just enough so that good students can understand the basic, and go straight into seminar and research math. I don't think a top student in sophomore year cannot understand or work on some combinatorics research problem and get some results, with proper mentoring and guidance.
  • deleted 20d ago
    [deleted]
• againstapples 21d ago
  At this rate AI will be doing all of the mathematics within 5 years, I don’t see why a mathematician would be worried about anything other than that at this point?
  • avsegal 21d ago
    Sure, but who will care? If no one understands it, it may as well have not happened. There's not much incentive to understand or internalize the results generated by AI. A human operator gives it a prompt and it produces some lean proof no one wants to (maybe can) read. Without the community of human mathematicians internalizing the proof, simplifying it, and re-communicating it to others we end up losing the main output of mathematics as an institution.
    • againstapples 21d ago
      Why would we assume AI will learn to solve millennium prize problems but will struggle with the easy part of doing the explaining? I think it’s too easy to predict that models 5 years from now will have the same limitations as the they do now, I would be amazed if this was true, GPT3 was the best model available 5 years ago.
      • avsegal 21d ago
        I'm not sure it's just a matter of explaining... If it's just explaining, than sure, that's something they already do well. The questions I have are: * is the structure of the generated proof even compressible/elegant to humans in a way that lends itself to being understood? * is it possible to transform the proofs to ones that are elegant without redoing all the work? * are there incentives to do any of this at scale? It's possible that a headline grabbing proof of a Millennium Prize problem generates enough incentive for people to simplify and gain understanding from it, but we run into problems when AI becomes the dominant approach for all of math. Although, maybe this is self-limiting? I guess it's possible we just ignore a bunch of AI generated proofs and only keep the ones people find comprehensible in a useful way. You can always hypothesize that at some point in the future (maybe 5 years? maybe later?) the models will be indistinguishable from humans and there will not be any functional difference at all. It's possible, but we're not there yet. And, as they say, past performance does not guarantee future results. Many technologies plateau at some hard ceiling of performance. Moore's law has had an unusually long run, but it's not a universal rule.
• picafrost 21d ago
  Academic research is a marvel because (aside from patents) nobody owns it, in the sense of property. It is given away to be used freely. Researchers want their work used and cited. The primary external reward for publishing is reputation and prestige which translates to remuneration for researchers. And that remuneration can be poor. Beyond the issue of growing understanding and keeping a bountiful stock of questions to pursue, this scheme seems to be threatened as well.
• pixelesque 21d ago
  Other than the fact it's mathematicians signing it, why is mathematics special in this regard: surely this generally applies to a lot of different industries and sectors of research / academia? Mathematics is being used as a benchmark because there are some high-profile awards in this area I guess, and possibly because 2/3 years ago LLMs were pretty atrocious at it so the level of improvement has been significant.
  • esafak 21d ago
    What's interesting is that these are the smartest people in the world, and AI is eating their lunch. You do the math -- pun intended.
• david-gpu 21d ago
  Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a painting could. He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts. Do you see some parallels as well? [0] https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiques/Salon_de_1859 https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiq...
  • matherial 21d ago
    I'm really tired of these arguments (this and "it's just like calculators"). Photography decimated other forms of visual art, so the concern wasn't wrong. But AI threatens the entirety of human intellectual endeavors. I can make do without oil paintings in my home. I'm not sure I want to live in a future where we make do without brains.
    • piker 21d ago
      Had me until the last word. Cameras did take away oil paintings, but not eyes.
      • astrobe_ 21d ago
        It did. While you're busy recording an "instagramable" moment, you are not entirely enjoying that moment. Your eyes are on the screen, not on the subject. In a way, if photography is an ersatz for painting that eventually made imaging available for the masses, then AI could become an ersatz for thinking. But it feels like I'm paraphrasing TFA. What will happen when AI companies have spent their advertising budget on math problems and whatever else gives the maximum wow effect for the bucks? Probably customers hooked on the vain satisfaction of spending token$ to impress friends.
    • beambot 21d ago
• KwisatzHaderack 21d ago
  Math, like art, it is more about the process and not the end result.
• TTorler 21d ago
  This is a Stephen Wolfram tier problem. I hope to read what he has to say on the matter in the near future.
  • saberience 21d ago
    Underrated comment
  • auggierose 18d ago
    His wife just died, so he might not be interested in that currently. On the other hand, he can probably use the distraction.
• fwlr 21d ago
  In internet culture there’s this phrase “Hydrogen Bomb vs Coughing Baby”, meant to highlight the absurd power difference between two combatants. In almost any scenario even tangentially involving mathematics, twenty-five Fields medallists uniting to denounce something would be a veritable Tsar Bomba. It should give you pause that here they feel like the ailing infant.
  • kzrdude 21d ago
    Well OpenAI took one step on the back foot at least, withdrawing from sponsoring this math hackathon event https://xcancel.com/danintheory/status/2098125701782372640 https://xcancel.com/danintheory/status/2098125701782372640
• k2xl 21d ago
  I’m sympathetic to the concern, but I’m still unclear on what the concrete ask is. If the worry is that AI companies are turning open problems into benchmarks and potentially “using up” fertile mathematical problems before humans can develop the ideas around them, what exactly should the companies do differently? Also why does discovering the answers preclude humans developing ideas from them? I don't get why solving a math problem stops anyone from doing that? Should they (AI companies) avoid training or evaluating models on open problems? Solve them but not publish the results? Delay publication? Only release proofs after mathematicians have had time to study them? Require some attribution or review process? The statement makes a strong case that “maximize the number of solved problems” may be the wrong objective, but it seems much less clear about what behavior they actually want from OpenAI, Anthropic, DeepMind, etc. I’d be interested in the most concrete version of the proposal. Without that, it starts to read a little like: "Please stop getting so good at our thing!"
  • HarHarVeryFunny 21d ago
    > If the worry is that AI companies are turning open problems into benchmarks and potentially “using up” fertile mathematical problems before humans can develop the ideas around them, what exactly should the companies do differently? Just stop doing that. Don't treat unsolved math problems as some cheap benchmark to beat. Leave the math for mathematicians, and let them use AI in a way that helps the field, not in a way that harms it.
• nonsensical_ 21d ago
  I’m trying to determine now if Terence Tao was a plant or a useful idiot. Maybe both.
  • azan_ 21d ago
    Care to elaborate?
    • nonsensical_ 21d ago
      Mostly that he really should have seen this coming. These people absolutely do not care what happens to mathematics (or any other field). They compulsively lie and steal and they played Tao and others like a fiddle. He danced to their tune and now that the music has stopped, now do they complain. He was the poster boy of the mathematician yielding these tools for his own benefit. But he forgot who the owners are. Too little too late.
      • kzrdude 21d ago
        You should read his comment from wednesday here: https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/comment-page-1/#comment-694321 https://terrytao.wordpress.com/2026/09/07/finite-time-blowup... And yes, at one point it gives you right about them taking advantage of him. He sat down for an interview and found later that they just used the "best clips" out of it for an OpenAI ad.
        • nonsensical_ 21d ago
          That’s table stakes!
• Art9681 21d ago
  This reads like people lamenting a bygone era and making a desperate attempt to bring it back. I'm sorry. Outside of the good ol' boys club, no one cares about some process they've romanticized simply because "that's how its always been done". Absolute nonsense. We are moving forward and if that means no human wins a fields medal because they didnt spend three decades working on a problem that could be solved in three days, the world will be better for it.
  • cyclopeanutopia 21d ago
    And who is "we" in your story?
    • deleted 21d ago
      [deleted]
  • suddenlybananas 21d ago
    Yeah who gives a shit about knowledge or understanding or insight.
    • robryan 21d ago
      You can still do all that. The only thing going is that in some cases the human isn't going to be able to claim that they made the key insights that first solved the problem.
• grumpopotamus 21d ago
  Could we develop new ways to develop understanding and explore new ideas, such as interacting with the models to explain and understand their proofs, as well as to brainstorm related directions to pursue?
• sim04ful 21d ago
  "We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose" Suppose we eventually have GPT-7-class models running practically on $100 devices, with their activity transparent, inspectable, and reproducible. At that point, what exactly is left for us to fear from this threat?
  • vatsachak 21d ago
    What's the threat? I would use it to write a dependent type theory that is JIT compiled and use it to rewrite emacs.
  • Centigonal 21d ago
    I've got to ask, let's say we get a small modular nuclear reactor running practically on a 1 acre lot, its design meltdown proof and waste-free, what then should we fear from this threat ? This is just a thought experiment. Jokes aside, any productivity-improving technology, even one with no negative externalities, has the potential to cause economic displacement and wealth concentration in proportion to the productivity gains catalyzed. Anthropic did a cool analysis of this for AI here: https://www.anthropic.com/institute/econ-scenarios https://www.anthropic.com/institute/econ-scenarios
  • deaton 21d ago
    The fact that those models are encroaching on things only human minds could do. Personally, as a human, I want there to be things humans are the best at, and intellectual things were the final thing that machines hadn't beaten us at.
    • buellerbueller 21d ago
      100% on board with this take.
  • TitusCaius 20d ago
    [dead]
• road61 21d ago
  It's a turning point for science and beyond. AI has shown itself to be transformative. Even today, it is already changing the how research in math (and other sciences) is conducted. In the near future, whether it is LLMs or some other superior method, its capabilities are only expected to grow. The time to ask the question is now: Will AI be arguably the best tool at scientist's disposal, or will it instead be paraded around as a super brain collective that no human or group of humans can compete with, discouraging entire new generations of future scientists from ever entering the field? The jury is out on this one.
• 12qqtt 21d ago
  Economist: "Are mathematicians talking their own book out of fear?" The Economist, who recently used "moral panic" now stoops to Hacker News AI booster level and inverts arguments usually directed against the rich and investors. What is next? The Economist inverting Upton Sinclair's quote to serve its billionaire owners? Look up the AI investments of the Agnelli family for example.
• throwaway1921 21d ago
  At some point someone is going to need to answer for "what happens when all intellect is hoarded by one or two companies?" It's pretty clear that these AI labs are basically stealing everyone's alpha.
• jokers132 21d ago
  Strange they are rallying against something their fellow mathematicians had a hand in creating.
  • Bengalilol 21d ago
    Let's focus on the subject and try to distinguish the technology and the frontier companies selling it. That's the key point in understanding the whole stance.
• nadermx 21d ago
  Back in the day you could think of a cool idea. I don't know maybe a plane that could fly without drag. To even see if this was feasable you had to understand physics, engineering, and then from there you had to have a math person see if it was actually possible. Now, I can ask ChatGPT about this and get back a proof that shows "a passive airframe cannot sustain zero-drag motion through still, viscous air" So, I think if anything now, Maths has changed for the better. More ideas can be proven false or true from a get go instead of wasting so much to see if its even feasible to find out it isn't. Progress if anything is about to leap frog anything we have ever known.
  • jaccola 21d ago
    This is a pretty moronic take. You only have to understand the first thing about physics (e.g., a 14-year-old's understanding) to know that a dragless airplane is impossible. If you are suggesting there is some new model of physics or groundbreaking technology that would allow such a dragless plane, then don’t let me discourage you! But AI won’t help at all, since it will only regurgitate conventional wisdom…
    • nadermx 21d ago
      Well, there is physics for an alcubierre drive, so these moronic takes have answers too.
• tmhn2 21d ago
  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.
  • num42 21d ago
    >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 https://www.youtube.com/watch?v=rB9YOi3lb7w and this: Daniel Litt - Working with LLMs to do high quality math https://www.youtube.com/watch?v=0wL8NlhxXcU https://www.youtube.com/watch?v=0wL8NlhxXcU
    • cubefox 21d ago
      > Dr. Tao said the same thing. Apparently he has since changed his mind.
      • ksoped 21d ago
• aaroninsf 21d ago
  Castle dwellers dismayed at moat-crossing technology. What's most important about this is that it's a case study of what happens when deeply evolved ecosystems are blown up by disruptive technology. The psychological and social and professional impacts and myriad and traumatic to be on the receiving end. Mathematics is merely one of the first domains disrupted. It will be unique only for being among the first... absent disruption of the entire civilizational project as a result of the disruption being caused. Woe for us that we try to navigate this degree of change at a moment when the very worst and ignorant and short sighted hold all the power, economic and political. Woe.
• fantasizr 21d ago
  AI bros here and elsewhere seem to come at Terry Tao with "not so smart now are you?" viciousness that is off-putting.
  • pfdietz 21d ago
    How dare they defend themselves when attacked by their betters. The nerve of those peasants.
• azan_ 21d ago
  I know that this comment section is not astroturfed, but it’s really uncanny how different comments are today compared with thread about solving navier stoke
• caaqil 21d ago
  The mathematicians would be wise to re-read The Bitter Lesson, maybe twice a day, until it sinks in. No offense and with all due respect to the Ivory Tower Giants but the whole "oh no you ruined the game because you solved it, I was supposed to play with that in child-like wonder manner and take several years to do so, and by then I would have showed you all the trickery I did to get there and maybe that will be useful to you" over the past 2 weeks is, get this, cope. Chess. Go. Coding. Now Math. Another one bites the dust. Let's meditate on this lest we forget: Stochastic parrots that generate the next-token cannot reason or produce anything meaningful. Let's protect our jobs at all costs, even if we have to drag all of humanity down. It can't be! Stochastic parrots can not replace the Ivory Tower. No way.
  • NateEag 20d ago
    You would be wise to take the time to understand a perspective other than your own.
    • caaqil 20d ago
      That you think I don't understand the other supposed POV is a limitation of your own faculties.
• jsrozner 21d ago
  For every benefit that sillycon valley has produced in the recent past, there have been many more harms. I am confident that this will be no different. Of course, benefits and harms depend on one's vantage point.
• jijji 21d ago
  another story about the lack of chain-of-thought reasoning traces in frontier models...
  • deleted 20d ago
    [deleted]
• G3nD 21d ago
  I kind of expected a sober stoicism from mathematicians. Feels silly in retrospect. This is just the math version of the "anti-ai" movement by "artists".
• fooker 21d ago
  Maybe mathematicians should be aligned better, rather than AI? The current measure of a successful mathematician is the problems they have solved or worked on. At some point in history, the measure of a successful scholar was how well one could copy manuscripts. Once we have a tool that starts to work well for this task, it's time to define success differently. It's a classic alignment problem! ;) But seriously, these people should start focusing on finding and proposing more important problems. And the credit of discovery should go to the person who defined a new category of important problems. It appears to me this is an incredible inflection point in mathematics, a neat forcing function like cryptography was for the development for modern number theory and algebraic geometry. Fundamental problems with great implications for other fields will be solved by AI because some entity would throw tokens at it. And these would be further built upon.
  • pfdietz 21d ago
    Another historical analogy: this is kind of like the transition from alchemy to chemistry.
    • fooker 21d ago
      Interesting analogy
      • pfdietz 20d ago
        The interesting difference between alchemy and chemistry was a change in the expectation of how results would be obtained and communicated. That is also changing here.
• qarl 21d ago
  Is this really any different than the problem in software engineering - where AI is doing the work of junior programmers and now they aren't getting the development they need? Seems the same to me. And it'll be the same in all industries soon enough. And then it won't just be the junior people. All the same problem: what do people do now?
  • f311a 21d ago
    It’s better to compare this to computer science, especially, theoretical one. LLMs stop people from exploring new languages, architectures and so on.
    • qarl 21d ago
      Well... computer science really is math already. :)
• drivebyhooting 21d ago
  All “fields medalist” signatories - a rarefied and elitist group indeed. I wish this letter could be more egalitarian and include the view points of those who AREN’T the beneficiaries of a highly competitive winner-take-all system. Since the common narrative is that AI frees up labor to do other things (engineering -> trades), maybe we can celebrate that genius mathematicians will now spend time teaching children how to be as smart as them?
  • youoy 21d ago
    Agree. That is also the part of the letter that does not make a lot of sense to me.
• Strilanc 21d ago
  This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal. So this letter's message will fall on deaf ears. Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction. They're knowingly risking the lives of every man, woman, and child to continue the work. The lives of their own sons and daughters. A person already rationalizing that isn't going to shed a tear for the careers of mathematicians. Just a bug on the windshield.
  • philipwhiuk 21d ago
    The point of mathematics is human understanding though.
    • Strilanc 21d ago
      That's only one of mathematics' many purposes.
      • falcor84 21d ago
        Exactly! What got me interested in memes as a kid is precisely the fact that mathematics is true in a way that is wholy independent of our understanding of it.
        • bonoboTP 20d ago
          Well, most kids are certainly interested in memes, but you got a really unique reason there.
          • falcor84 18d ago
            Oh, sorry, I of course mean to write math and autocomplete hit. To late to edit now, so I suppose it'll remain as a happy accident.
• nonsensical_ 21d ago
  Both Amodei and sama are weeping at this news. The horror. The horror.
• heyitsdaad 21d ago
  An experiment I would like to see: Train an LLM with no advanced math texts: only basic math up to 6th grade, conversational text and literary works. Interact with it (you cannot refer to anything past 6th grade math since you don't know it yourself) and get it to propose a solution to a real world problem. e.g., come up with RSA to practically secure communication.
• WarmWash 21d ago
  And here we all thought for sure that it was gonna be the "dumb" work to fall to the machines first. Human hubris really is something...
  • pfdietz 21d ago
    Hans Moravec likely isn't surprised by this.
• gwd 21d ago
  This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It turns out having an oracle for the "right" answer in chess, even without an explanation, used properly, allows humans to develop broader, more accurate insights. The argument here sounds similar. The fear, as I understand this statement to be saying, is that by being given the correct answer, in the form of a 100-page Lean proof, humans will be robbed of the chance to from insights about the structure of mathematics itself. I don't see any reason that humans can't continue to develop insights as they try to digest the 100-page Lean proof into something more manageable; but with more certainty and fewer false starts.
  • tossandthrow 21d ago
    I like this approach. A but like whenever the first sprinter hits a new world record other runners follow along. Knowing that something is possible tends to strengthen our ability to work with it. We will potentially see the same with math.
  • fantasizr 21d ago
    => If chess.com was worth billions and Daniel Rensch was threatening everyone to do what he says.
  • senfiaj 21d ago
    Well, chess is a sport where humans are supposed to compete. But math, programming, science are mostly not, and AI might affect economy, careers, etc.
    • magoghm 21d ago
      That's correct. As far as I know nodody builds any kind of science or technology on top of chess, but mathematics is at the base of most science and technology. It would be horrible if we prevented AI from solving mathematics problems, just because mathematicians want to solve them by themselves the "hard way".
• jrowen 21d ago
  This kinda reminds me of the documentary about the top Go master that got beaten by a computer in dramatic fashion and had an existential crisis. Man confronting his own limitations in the realm he previously ruled unchallenged, what a time to be alive. Nobody is going to care that the math isn't being done in the traditional way. The results speak for themselves, this is now a part of the landscape. No amount of hand-wringing is going to put the cat back in the bag. Adapt or perish.
  • NateEag 20d ago
    > No amount of hand-wringing is going to put the cat back in the bag. Adapt or perish. We can and have put some ugly, hissing, spitting cats into bags, some of which weren't even in one to begin with: * Chattel slavery is illegal, and the vast, vast majority of humans agree it's appalling it ever wasn't. * Food manufacturers in the US are no longer allowed to put highly-dangerous additives to their products and hide the fact. * Women are allowed to vote. * Ten-year-old children are no longer being maimed and dying in American factories. Claiming it can't be done is either fatalism or propaganda for execrable companies whose evil has rarely been matched in the history of capitalist business. Do I have a clear solution for how to stop the insanity? No, not yet, but that is not a proof there's no way to do it. You can of course choose how to spend your time in this world, but I don't see the value of either 1) assuming we're screwed and giving up before trying to fight, or 2) shilling for lying assholes like Sam Altman.
    • jrowen 20d ago
      Thank you for this response, and I will clarify. I would roughly lump all of those into "social issues," whereas I would put "using AI to advance math" under "technological progress." That's why one article likened it to Socrates's fear of the written word. In broad strokes, I would say that once a technology becomes available, no amount of social pressure will stop it from proliferating. If there's a distinction being made between "using AI for math" and "the particular methods being employed by OpenAI", I think that's splitting hairs. The core of the issue is that math is being done outside of people's heads by a different thinking system and they're worried about the implications. If you look at something like the EPA (or the FDA as you mention), it is true that certain uses and side-effects of technology have been identified to be detrimental to society and have been restricted, but this letter doesn't seem to be in that league, it really seems like sour grapes to me. Dumping toxic chemicals into the water table is one thing, saying "we don't think people will learn from these methods in the same way that they traditionally have" doesn't hold as much water to me.
• buellerbueller 21d ago
  Terrence, youre a mathematician; now extend this to the general case: AI is misaligned (inherently) with humanity.
• sim04ful 21d ago
  Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ? Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ? Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, reasonably un-constrained by any institutional interests. What say the 1% ? Lifted up my comment for addition visibility
• doubtfuluser 21d ago
  Im surprised about the sentiment in this discussion. I totally see the problem Terence is describing. We are loosing a lot in understanding and focus if it continues like that. The solution found for Navier Stokes doesn’t have much „real value“ - but what almost always happened in the past when people worked on the difficult problems, these sparked new ideas / new theorems that broadened our knowledge. Think back at your grad studies, figuring out a proof as homework was hard, sometimes incredibly hard, but while doing it we gained a lot of understanding how things work. Now asking AI for the solution and „just“ getting it, risks our understanding, our creativity and our ability to connect the dots with other territories. I see it in students nowadays, there is much less understanding, much less creativity in finding solutions. I truly think this „short-path“ solution with the „death of struggle is one of the biggest risks with AI already for human development
  • kansface 21d ago
    Some people are just out there doing automated math proofs for reasons. If you want understanding, value, and edification, that is on you, not them.
  • nullbio 20d ago
    His complaint is a very weak argument. If the complaint is about AI just giving answers and not good understanding around them, or frameworks that lead to more solutions from them, then that means there is a gap that can be filled by human mathematicians. So all the AI has done has actually made mathematicians lives easier and provided them with an opportunity to fill that gap. They should be using it to do that, instead of complaining. In fact, I would bet if this gap were not present, it'd be an even worse complaint: Now we have absolutely nothing to do in the field.
    • kaffekaka 20d ago
      You have a point, but I think a concern is that the environment in which to fill this gap is threatened since the unsolved problems have functioned as a guiding lighthouse and measure of progress. Frankly: will someone pay for mathematical research to understand things we already have proofs for?
• throwaway713 21d ago
  Contrarian take: I think the ability of AI to produce valid mathematical proofs (even inscrutable ones) is absolutely fantastic. Mathematics as a profession does not have a monopoly over math itself any more than professional pianists have a monopoly on who plays piano, when they play, and how. I have sympathy for any jobs that might be affected (much as my own job has become more tenuous in software engineering). And if the field is disrupted by chaos that makes the research process unproductive, that's bad too and should of course be handled by applying better organization within the institutions that tend to perform mathematical research. But to a large degree, the notion that "sloppy AI proofs are bad for mathematics research" seems like a total failure of the imagination to me. Attempting to find shorter proofs or more elegant proofs can be turned back in on itself via proof theory. There are proofs in Presburger arithmetic that are doubly exponential in the length of the sentence. Yet a more powerful theory like PA makes quick work of such theorems. The explainability or "subjective beauty" of a proof can be quantified and optimized against. Optimization itself can be optimized against. I really don't understand how this magical ability to know the truth of more theorems much more quickly—even via an "ugly" route—is anything but a net positive.
  • auggierose 21d ago
    Yes. Mathematicians don't really get logic, and Tao is no exception.
    • throwaway713 11d ago
      I've been thinking about this comment for a few days; was it intended to be serious or facetious? I wasn't criticizing Tao in any way. I just think there's a lot of interesting work that's not in his primary domain of study for which AI has some potentially non-obvious benefits.
• BeetleB 21d ago
  Lots of Fields medalists signing this. Interesting to see one not there: Timothy Gowers.
  • Rzor 21d ago
    Interesting indeed. He talked about this imminent crisis a few months ago. https://xcancel.com/wtgowers/status/2052830948685676605 https://xcancel.com/wtgowers/status/2052830948685676605
  • onethought 21d ago
    nor Andrew Wiles
• johnsmith1840 21d ago
  They can get with the program or be the equivalent of a genius SWE writing assembly on punchcards in 2026. The only thing I read from this is their ego being bruised by a machine. If these people cared more about discovery and advancement of human knowledge the only thing they should be doing is celebrating. There's no proof of plagarism but that's an independent issue. How are they not realizing that in the future children will be able to do impossibly hard math but they will be doing something we can't even think of as of now. One world class mathematician in the future could be advancing mathematics the equivalent of one Riemann hypothesis A DAY. How are they not celbrating this as the achievment of the centry? Who cares about plagarism at this scale. It has been solved and it wouldn't have been without AI.
  • nancyminusone 21d ago
    for the same reason why you do not get full credit for only writing down an answer without showing work in an exam.
    • johnsmith1840 21d ago
      lol what a bad analogy. Why should anyone care how much effort a result takes to achieve? If anything our entire world functions because we reduce that effort as much as possible. I don't judge you for not growing your own food when you hand me a burger.
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• _zoltan_ 21d ago
  Welcome to the new world. I, for one, welcome our new math overlords. :)
• adastra22 21d ago
  Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. Alternatively, some claim that mathematics is about understanding these implications. Under the first definition, AI is already, and forevermore will be faster and better at proving theorems. Just like it is better at checkers, chess, and now go. The author asserts that AI proofs are incomprehensible to humans, and so under the second definition AI is merely a tool to overcome one hurdle on the way to understanding. So which is it? The author seems to claim the second definition, but bemoan the end of mathematics under the first.
  • loglog 21d ago
    > Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. That's like saying that programming is about producing valid programs in various programming languages.
    • adastra22 20d ago
      It is though. I am not being edgy. Programming is about making valid programs, yes. I literally have no idea what else you might be gesturing towards.
  • youoy 21d ago
    Dont confuse mathematics with the formal system. If you beleive mathematics = formal system then AI is obviously better at it, and we dont need humans. But then who decides why a statement is mor important than another? In the eyes of a formal systems all statements are born equal.
    • adastra22 20d ago
      I didn't know some statements in math are more important than others?! Some are more useful, and that is something you can quantitatively ask.
      • 20d ago
• bobzowak 21d ago
  This is really only a short-term problem where the AI companies only have the internal models that can solve these. In the “long” term, which could honestly mean months, everyone will have access to Bel/C/D-level models capable of solving these anyway.
  • nojs 21d ago
    This. Like programming, the community will shortly be forced to come to terms with a lot of new self-proclaimed mathematicians “vibe-solving” problems and dumping solutions without understanding them. It’s not really a special case for mathematics.
    • pfdietz 21d ago
      That's going to force formalization to become required for any new result to be taken seriously.
• manlymuppet 21d ago
  What changes exactly is this post asking for?
• yieldcrv 21d ago
  solving the problem is aligned with humankind
• waffletower 21d ago
  Tao's calls for respect for provenance in mathematics publication are laudable but most likely naive given the closed nature of frontier model training data curation. Anthropic and OpenAI may react with a symbolic and short-lived olive branch, yet provenance is a larger issue that has impacted other fields beyond mathematics. While traditional respect for lineage in mathematics is of value to the academy, industry and science at large will likely be much more Machiavellian about such concerns. Mike McCoy's recent article is also timely (https://mbmccoy.dev/posts/mathematical-conservatory/ https://mbmccoy.dev/posts/mathematical-conservatory/). The parallels to the music conservatory are quite telling -- academic music describes a musical culture in preservation that has completely lost touch with musical developments beyond the early 20th century. Mathematics may very well evolve separately and with very different values than the academy upholds. The crisis of music at the academy is a cultural disconnect and a serious loss of critical analysis and acknowledgement of widespread and dramatically evolving music practice; however, for mathematics, the impact would have much more severe ramifications for education and human development if the academy forces a schism with AI. As models improve they very well may be inventing mathematics -- science and engineering may grasp for them -- they'll exist with or without attribution. Would be a shame for the academy to land on the wrong side of history and refuse stewardship of upcoming AI-assisted mathematics, including provenance, because of this misalignment. If attribution is important, then the academy will set aside the institutional resources to do it. If you succeed at having model developers participate, I commend it. To let mathematics be born in isolated context windows and only serve narrow, localized engineering purpose without rightful addition to the canon, would be a tragic, yet preventable, loss.
  • sabujp 21d ago
    thank you for this commentary, as a violinist / software engineer / "computer scientist" / "mathematician" i can see that studying and doing math will still remain a thing that humans have to do to train their own brains to think and to form better neuronal connections. We may not get paid to do it anymore but it will still be important for our own development for the same reasons orchestras and bands still exist in elementary schools and beyond (at least in many parts of the US).
• hbcdbff 21d ago
  I have never, and I mean never, seen such a declaration have any effect whatsoever.
• modeless 21d ago
  Taking a snapshot of the state of AI math right now and concluding that it will be net negative to human understanding and insight in the future is very short sighted. This statement will be used to promote ideas and actions that will ultimately be disastrous for our country.
• manlymuppet 21d ago
  Somewhat unrelated: is it wrong to say mathematics is not art, and that there is always a right answer? I know that's not romantic, but maybe it's true. Before LLMS, programming was something I might've said required creativity and human input to do properly. It's not that creativity or human input isn't valuable anymore, but AI has forced me to realize that coding is much a means to an end, and that all things considered, the end matters much more than the means. If we can make important mathematics progress faster and better with LLMs, I think it's wise not to fret over an apparent loss of our humanity. Perhaps that's only a loss we want to have.
• pelican0 21d ago
  Given the existence of this technology now and the incentives of the AI companies, both of which are not going away; what's a good future here? A major part of the complaint is that there's no conceptual understanding and building of new ideas coming out of the AI proofs, thus defeating the purpose of the original pursuit. If in 2027 the AI models start producing, with every mathematics or science breakthrough they make, well-written documents tailored for human understanding, with intermediate concepts, expositions of failed-but-once-promising paths, etc. Would that be good alignment with the mathematics community?
• iamkeithmccoy 21d ago
  There's a reason mathematics is generally within liberal arts programs rather than science programs. Mathematics is the art of logic. Yes, sometimes mathematics becomes incredibly useful but most mathematics is never applied. Compare that with computer science. Most of the work we do in software engineering is in service of an applicable output - software products that facilitate processes or bring in revenue. Turning up the dial on AI gets companies to these outputs faster. Turning up AI on mathematics helps solve conjectures and can provide new insights. But it has a major misalignment with the purpose of mathematics which is largely intellectualism.
  • exhaze 21d ago
    You are referring to Boubakhism, not mathematics. “Mathematics is a part of physics. Physics is an experimental science, a part of natural sciences. Mathematics is the part of physics where experiments are cheap” - Vladimir Arnold On the matter of computer science having anything to do with computers, please refer to Djikstra. It’s about computation, not computers - an application of mathematics, predominantly thanks to Turing, Von Neumann, and Claude Shannon’s masters’ thesis; though ofc many others as well but I see them as three individuals who made the minimal structurally necessary contributions - VNA and silicon are one of many possible substrates. Also in the service of others around us.
  • azkalam 21d ago
    I think it could be useful to know something like P=NP, even if we don't understand why.
• deleted 21d ago
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• exhaze 21d ago
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• whatever1 21d ago
  At some point we will lose track of all the ai discoveries that are worth remembering. Academia with the publication system had a way of retrieving old discoveries and build upon them. If my LLM session found something groundbreaking in between the billion tokens it produced, how would you ever know?
  • pfdietz 21d ago
    LLMs are excellent at doing searches of the math literature; presumably they'd also be good at doing searches of AI-generated results.
  • tejstead 21d ago
    I think this is why Terence Tao created https://palomar-registry.org https://palomar-registry.org (I have no affiliation with them besides also having sent in a result there)
• cat-whisperer 21d ago
  chain of credit is important, and plagiarism is harmful. But is science/mathematics ultimately a pursuit of knowledge, or a pursuit of recognition? Recognition helps keep people motivated, but that shouldn't be the pursuit of science or mathematics.
• Absonsonson 21d ago
  For some reason, every time I see something like that, I get major Ted Kaczynski vibes.
• Animats 21d ago
  There's an unpopular branch of mathematics which does not have infinities - finiteism.[1] The constructive version of finitism takes the position that there is no such thing as infinity, just arbitrarily large upper bounds. You can have theorems about arbitrarily large numbers, but you never get 1 + 1/2 + 1/4 + 1/8 ... = 2 The benefit of finitism is that it escapes undecidability. The big objection to finiteism is that it's a lot more work. Infinity swallows many special cases. Proofs get longer without infinity, and most of the special cases are uninteresting. That's not a problem for AIs. Someone may start up an AI and make it grind through Hilbert's program for putting mathematics on a fully consistent foundation, starting from a finiteism base. This is a huge, unrewarding job. Great for machine work. [1] https://encyclopediaofmath.org/wiki/Finitism https://encyclopediaofmath.org/wiki/Finitism
  • feoren 21d ago
    > 1 + 1/2 + 1/4 + 1/8 ... = 2 It's not necessarily clear that this statement requires infinity, if you're willing to treat "... =" as a shorthand. You might prefer something like "1 + 1/2 + 1/4 + 1/8 ... -> 2" if it's more clear, where "->" means something like "gets as close as you like without ever getting further away than that", but really the "=" sign is already overloaded in all sorts of subtly different ways anyway, so there's not really any trouble using it here. Almost any rigorous definition you can write down of exactly what that statement means would not rely on the use of infinity.
    • Animats 21d ago
      See this introduction to limits.[1] If you allow infinite recursion, you soon get to Godel and undecidable problems. Finite deterministic systems are decidable, because you can in principle enumerate all the states. The halting problem is decidable for deterministic systems with finite memory. It may be exponentially hard for some programs, but that's quite different from being undecidable. (This is too long a subject to discuss here, and I haven't worked on constructive mathematics in many years. It's more practical than it was decades ago. You need power tools, which we now have.) [1] https://www.mathsisfun.com/calculus/limits.html https://www.mathsisfun.com/calculus/limits.html
  • 21d ago
• lbrito 21d ago
  >Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. That's just capitalism seeping through a previously unexplored crack into academia, and attempting to do the only thing capitalism knows to do - maximize profits - with no additional concern.
• ex-aws-dude 21d ago
  The thing is no one is stopping anyone from getting the same knowledge/understanding/insight If those things are disincentivized because the original problem is “solved” and there is less prestige to motivate people doesn’t that say more about issues with the community of mathematicians than the AI
• HarHarVeryFunny 21d ago
  That has to be the most impressive endorsement list any declaration has ever seen! 25 Fields medallists! Wow!
• frozenseven 21d ago
  Knowledge is not a private guild. And this revolution will not stop just because you're upset. What can be solved, will be solved. And that's a good thing.
• moktonar 21d ago
  OpenAI should just apologize for having been too greedy. That’s it, as simple as it gets. The fact that it never will is the biggest red flag.
  • pfdietz 20d ago
    OpenAI didn't do anything wrong. Why should they apologize?
    • moktonar 19d ago
      They took a lifetime of research effort, threw millions of dollars of compute at it and claimed their AI solved a MPP, and they did all this just to be the first to claim the prize. Once you knew the direction, given the new insights on the subject, with all that compute you could probably have just bruteforced your way to a solution, and thousands of agents are not the same thing as “our model came out with a solution on its own”. This is pure greediness, and require at least some apologies to the involved researchers and to the whole community for showing such bad ethics and behaviour
      • pfdietz 19d ago
        I looked through your words and didn't see anything they should be ashamed of. It seems like you're trying to construct from mental vapor some justification for your prejudice.
        • moktonar 19d ago
          Ruining a lifetime worth of research effort, passing bruteforce as achievement, thus lying, just to appear first in position, is something to be ashamed of IMO.
          • pfdietz 19d ago
            Researchers don't have any obligation to not ruin the work of others. Research is a competitive arena, not kindergarten. Disparagement of the effort as "brute force" is just argument by insult. What matters is the result obtained. You don't like how they obtained it? Cry me a river.
• ggm 21d ago
  To me, the "meaning" of proof is twofold. First is the understanding which is completely absent from a proof which depends on exhaustive iterations of instances or is asserted by fiat from myriad individually contestable paths. That's what I think makes AI proofs risky: they absence of understanding. The second is the utility. We get to do navigation because the maths about angles and spheres checks out. The social utility downstream of AI proofs may be huge. I don't like this disjunction.
• andai 21d ago
  So what's the actual point here? It's too fast and we can't keep up? Isn't that just a function of the technology itself, and the same problem being faced by every other field? And going to get exponentially "worse" every year! Or is the issue that they're bad at explaining things, in a way that produces actual learning? (e.g. AI is amazing for learning but the net effect on students so far appears to be negative.)
• newprint 21d ago
  The level of things happening in the last several months is just SciFi level, especially last two weeks. 1. Overlords of AI threatening to destroy someone if their demands aren't met over the Millennia problem. Proving the point that given the chance, owners of the AI companies will immediately use their power to squash or control other people. (See Butlerian Jihad) 2. At least for me, the Exponential progress didn't sound true until this week. If AI indeed solved all those problems and proofs and solutions are correct, we went from "Write me English 101 college essays" to "Help me solve the Navier–Stokes existence and smoothness problem" in a just 3-4 years. 3.Looks like someone's work might have been stolen, by AI company and there are strong evidence. See point 1. 4. War between AI & AI companies. 5. It produces a machine verifiable LEAN proofs for the hardest problems know to us !!! Proving that point that best use of AI so far is to create verifiable systems. I.e the absolutely chaotic AI creates verifiable (orderly) proofs. It is Maxwell Demon: chaos to order.
• clintonc 21d ago
  I agree with many of the sentiments here. But an open letter signed exclusively by Fields Medalists that purport to define precisely what the "mathematical community" (who is inside and outside) and what their goals are raises my hackles for some reason. It is true that the manufacturing of "true/false" statements is not the same as gaining understanding of a problem. However, for many mathematicians, true/false statements are already manufactured by others. Think of a student who is given a conjecture to investigate, with their advisor describing it as "it must be true". Most exercises in a textbook are stated such that the outcome is known before you begin. That's not really a problem -- investigating the conjecture/exercise yields its own dividends, whether or not the outcome is known. It is also the case that defining new directions involve understanding and synthesizing related problems, asking the right questions, and deciding upon the right directions, and it's not clear that AI can do that at all. The real risk, I think, its the public's (and funding agencies') perception of the importance of "human" mathematics, but that's already a struggle. For example, it's tough to explain to the lay person why it's still important to research group theory -- the main example people cite is RSA encryption, which was invented almost 50 years ago.
• keeda 21d ago
  I understand this stance and where they are coming from, but I can't help but think this sounds very analogous to engineers' arguments against AI-assisted and vibe-coding, especially with regard to cognitive debt. Yet the software industry is plowing ahead, reportedly pushing mountains of unreviewed code to Prod, and the world hasn't ended. Of course, nobody's really comfortable with it, so this is also a forcing function for the industry to adapt and figure out new techniques to manage complexity and trust. I think the same will happen with Mathematics. But it is also possible we will end up with three forms of Mathematics: the one we understand, the one we don't, and the one we don't understand but can prove to work. Kind of like magic -- with all the positive and negative connotations of the word. It is pretty evident that these models will soon exceed our cognitive capabilities. Is it right to hold them back just because we can't keep up? Many of those discoveries will be so beyond us that we can't do anything with them, but that also means they can't hurt us. On the other hand, there could be many discoveries that we can parlay into practically useful applications, even if we don't understand them. Just like LLMs.
  • Creamsicle47 21d ago
    > Yet the software industry is plowing ahead, reportedly pushing mountains of unreviewed code to Prod, and the world hasn't ended. Yes, this has gone so well
    • ls612 21d ago
      It really has. All of the places facing an unusually high outage rate are places that have seen huge growth in their service usage (Anthropic, GitHub, etc) which is to be expected. The rest of the world has been happily chugging along with coding agents for almost a year now and things seem to still be working just fine.
      • Creamsicle47 20d ago
        > All of the places facing an unusually high outage rate are places that have seen huge growth in their service usage (Anthropic, GitHub, etc) which is to be expected. That's not true, many of these outages have been directly attributed to AI tooling. > The rest of the world has been happily chugging along with coding agents for almost a year now and things seem to still be working just fine. Many more services are now being attacked by AI agents that originate from all kinds of organizations including OpenAI, Anthropic, and many others. Unless you're purposefully being obtuse, I would not call that "working just fine".
• andai 21d ago
  I note here an isomorphism with my essay from earlier this year, The deliverable is you! Programming as theory building: A program is not the only output of programming. The other, arguably far more important output, is the programmer. When you write the program — with your own hands — the program is proof that you have a solid mental model of the program. When you let the computer write the program for you, the program is proof of … nothing. https://nekolucifer.substack.com/p/the-deliverable-is-you-programming https://nekolucifer.substack.com/p/the-deliverable-is-you-pr...
• ThoAppelsin 21d ago
  Maths will continue as a field of natural science in understanding the results and uncovering meanings in them. It is normal that the established community is afraid of the change, because it’s their _home_ that’s changing. But it will be a better home to the new generation nonetheless, one that’s not as daunting as the higher maths has always been to many. The concerns raised here will not be a problem at all.
• lukewarm707 21d ago
  i was initially optimistic that ai could be distributed. having this technology in the hands of many would counteract the malign elite who would use ai to oppress the rest of humanity. in the meantime given that intelligence is scaling proportionately with inference time compute, we are concentrating far too much power in the hands of the few who have both their own model and datacenter. putting this amount of power in the hands of so few would require leaders of immaculate moral integrity. what we have in the US at least is an emergent kleptocracy with obvious dark triad traits: sam altman, dario amodei, elon musk, etc. they are malign and will use this power for their own benefit, at the expense of others. ignore pleas of public benefit. look instead at the evidence: infighting, systemic dishonesty, reckless disregard for safety, political lobbying and manipulation, putting power in the hands of the elite few in the guise of safety, using ai in the military to oppress and inflict violence on others. really to prevent a bad outcome, we would need to act soon enough to prevent the kleptocracy from corrupting politicians and democracy with them. i would ditch the claude or openai subscription and support open models instead, preferably in countries outside the US to prevent global neocolonialism.
• MrDrDr 21d ago
  Is the purpose of mathematical research to understand the ‘truth’ of numbers? or be the person who find that truth? I think people who are interested in finding the truth won’t care where it came from.
• petilon 21d ago
  > We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. This is Terry Tao talking about AI's impact on Math, but this could just as well be a software engineer talking about AI's impact on software development. Do mathematicians deserve more job security than software engineers?
  • RGS1811 21d ago
    It's not about job security. It's about the social and intellectual practice of the discipline. The threat to mathematics isn't that suddenly the profitability of their profession (lol) is going to go away, it's that people are thinking of AI as a replacement for the human social and intellectual practices that constitute the discipline.
    • 2snakes 21d ago
      Kinda crazy to think that academia functions as a kind of humane reverse centaurism. Theory X (reverse centaur) before Theory Y (centaur) for managing the development of others.
    • petilon 21d ago
      > The threat to mathematics isn't that suddenly the profitability of their profession (lol) is going to go away, it's that people are thinking of AI as a replacement for the human social and intellectual practices that constitute the discipline. You could say the same about software development. Software development is a group effort, so it includes social practices, and certainly includes intellectual practices as well. For the sake of argument, how is this different from the Luddites? The Luddites feared that machines would displace not only human labor, but also the social knowledge, skilled judgment, and craft traditions embedded in their work.
• fasterik 21d ago
  It's good to start a conversation, and the number of Fields Medalists behind this certainly lends a lot of weight to it. But I'm not seeing a strong argument for misaligned incentives beyond the specific plagiarism allegations. The job of an AI company is to build systems that solve problems. The job of a mathematician is to advance the state of human knowledge. If anything, an influx of solved problems should increase the demand for human mathematicians who can convert them into conceptual understanding.
• youoy 21d ago
  We should create a platform where people can upload AI slop proofs anonymously without taking credit for it. That way the incentives of planting a thorem flag would go down. And if someone wants to clean an AI slop proof to advance the field, they can do it without cleaning the house for free of the person that planted the flag. Would OpenAI have uploaded their proof to such a platform? If you know the answer then you know what the problem with what happened is.
• deleted 21d ago
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• seizethecheese 21d ago
  I don’t think they make a coherent argument here? This seems to hinge on some argument that because AI doesn’t properly explain its breakthroughs, therefore the breakthroughs are less fertile for human understanding? This makes no sense. Why wouldn’t these under-explained breakthroughs be extremely fertile soil for explanations? Imagine time traveling back in time and offering Leibniz a packet of proofs from the intervening years, but with the caveat that there would be no explanations. Would he say no?
  • geraneum 21d ago
    > Would he say no? And that’s the issue the article is trying to explain.
    • seizethecheese 20d ago
      My thought experiment was trying to extract the issue from the zeitgeist around AI, so not really
      • geraneum 20d ago
        There’s answer for you there if you’re willing to see it, whether you agree with it or not. So there’s that.
  • atomicthumbs 21d ago
    Because the fertile soil comes from the process of reaching the breakthrough. This should be fairly obvious.
    • seizethecheese 20d ago
      I don’t think it’s obvious. In my Leibniz example, mathematical understanding surely would have accelerated right?
• semiinfinitely 21d ago
  Jacob Tsimerman fields medalist notably missing from the list now works at OpenAI but recently admitted to be "grieving" for mathematics 1. https://youtu.be/6uIJdXmB4vE?si=5QMN5Dos7EE7WlrB&t=154 https://youtu.be/6uIJdXmB4vE?si=5QMN5Dos7EE7WlrB&t=154
• oktaygoktas 21d ago
  The main fear seems to be that if mathematics is done at this speed and in this way, humanity will lose its intuition for doing mathematics.
• Danox 21d ago
  Touché… In short you still need the humans to understand what’s going on at the end of the day whether it’s a mathematical equation or source code for a computer program relying upon mindless AI isn’t good enough. Humans still have to do the thinking or is it in the brave new world the error checking at the end of the day?
• taurath 21d ago
  I find this explanation has a lot of applications for programmers within companies. It’s one thing to get your LLM to give an answer, it’s another to bring a group of people into shared understanding of a domain.
• Bengalilol 21d ago
  As I understand the article, its title should be: "A Severe Misalignment of AI Frontier Companies with Ethics."
• lll-o-lll 21d ago
  > We are witnessing a general threat to intellectual work This is the crux of it and goes far beyond Mathematics or Computer Science. To get a bunch of humans to do anything, you have to motivate them. Kleos and Timē; renown and stuff. These AI companies threaten to rip this away from everyone but themselves, and this recent millennium prize is the perfect example. Solving this problem as a human would have led to tremendous Kleos; my name would be written in the annals of mathematics, lecture tours of praise were mine to be had for the rest of my days. This one victory would have earned my recognition throughout history. The greatest a mortal may hope for. Ripped away. It would also have given me great Timē. The prize money, the professorships, the book deals. Gone. If all hope of “renown and stuff” in the intellectual realm is now taken by the AI companies, they will remove all human motivation to pursue these endeavours. Perhaps the glory will come from slaying these fell beasts.
  • dhbradshaw 21d ago
    These are both big motivations but not the only ones. But there's still play. There's still curiosity. And there's still the drive to understand something for yourself.
    • lll-o-lll 21d ago
      > But there's still play. There's still curiosity. And there's still the drive to understand something for yourself. Yes, but think about what that implies if those are the only motivations left. Gone are the professions. Gone are the ambitious. There is plenty of space for people to work on intellectual pleasure pursuits (as there is with art and music), but the death of all intellectual based industries is still something to avoid. Or to mourn.
      • noslenwerdna 20d ago
        Good? Those people were in the field for the wrong reasons. No reason to mourn them leaving
        • 20d ago
• kzrdude 21d ago
  I wonder what Demis Hassabis thinks about this. I thought he cared a lot about mathematics.
• HamedAlkhateeb 21d ago
  Nothing AI companies will change the value of math, as William Thurston said: The product of math is clarity and understanding, not theorems by themselves. What they seek for the IPO is devilish and misleading, and doesn't serve the true purpose of the math.
• impulser_ 21d ago
  Are we here to solve problems or are we here for prestige? Who cares how the problems are solved?
  • cyclopeanutopia 21d ago
    It's more about *finding* problems. And soon there won't be anyone who can do that, thanks to people lacking imagination.
• woopsn 21d ago
  My interpretation is they don't care about scooping mathematicians they were just trying to scoop a competitor. They had a short window in which to complicate Anthropic's priority, when Anthropic announced be able to say "ok nice but we did that too". Upon realizing they'd misunderstood, incredibly they said to this academic (who did not resolve NS) okay well just go ahead and claim the prize, so long as you're not Anthropic let's make this a good story. If you spend $20M working out a Millennium Prize problem, in what universe would you offer that an unrelated effort should take credit? This is a branding game rather over whether software engineers are going to use codex or claude. In that light $20M (or whatever it was) might be worth it to squash even the rumor that claude code is more capable. Engineers look up to mathematics, while at the same time business and probably most engineers think the problem was to solve the problem. GPTs solved one the hardest known problems so they can solve my company's problem. Some go further looking at these people, very on-the-nosely likened by one commenter here to ants, talking about education and responsibility and "core values" etc and just don't care. There was a major problem at the beginning of the week that is not a problem now and that is uncomplicated progress. It's not wrong for OpenAI/Anthropic to do math for product development or even just branding but seemingly at no cost now they could work in an arena real mathematicians aren't interested in, versus just mowing the field. Everyone involved on their side should admit the purpose of these demonstrations is not to engage mathematical ideas it's about Claude/Codex. there's no shame in that. Which is better at solving random hard Diophantine systems? That would seem to tell me as much as I need to know insofar as a model's value is represented by raw mathematical power - then, take my money just as well! Assuming the worst accusations are not true I think there are ways forward going to be acceptable for all. The labs themselves do not represent Terrance Tao as some kind of gate-keeping dinosaur in this. They're not interested, not the kind of entity that can care about theoretical mathematics. These dudes are paid 7-8 figure salaries ultimately for the product, they solve a Millennium Prize problem then pretty quickly seem to move past it.
  • blharr 21d ago
    >they weren't trying to scoop a mathematician they were just trying to scoop a competitor Well. Obviously, yes. But in doing so they still DID scoop out a mathematician in a very unethical way. In doing so they showed that they basically have a huge gun they can point at X work you care about and develop, and can cut you across the finish line. And take credit for it. Obviously this already _existed_, but is just much more significant because even a rumor can be converted into a complete takeover of a discovery. > They're not interested, not the kind of entity that can care about theoretical mathematics. These dudes take home 7-8 figure salaries, they solve a Millennium Prize problem then pretty quickly move past it. I get your point, they don't really care about solving all the maths problems. But they're still going to solve them for clout and profit motives. Up until it stops wow-ing people... at which point they will have likely decimated the frontier of the field. And this is kind of the root of the entire concern. They will move into the forest and completely steamroll all the problems, then declare victory and move on, leaving only pavement and asphalt behind.
• moralestapia 21d ago
  There's massive cope and then there's this. I've never been a fan of Tao et. al, so I'm glad he's being wiped out. He'll do fine anyway, doing conferences, etc. Also funny they deliver that on vibecoded site, lol.
  • esafak 21d ago
    Which mathematician's take on AI do you like? Do you think mathematics should no longer be an intellectual pursuit?
    • moralestapia 21d ago
      I haven't heard about his take on AI (sorry about derailing a bit), but generally I like Robert Ghrist's approach to life and math. I'll check out if he has said something about it. Interesting guy.
      • deleted 20d ago
        [deleted]
• chrisjj 21d ago
  For such great minds, they seem to be rather muddled thinkers. E.g. of the actually three misalignments in this complaint, the jey one seems to be: "The goals of the AI companies and the goals of the mathematical community are severely misaligned." And that's wrong. There is no misalignment. Each is independently aligned with its respective interest. And those two interests diverge - just as you'd expect.
• AIorNot 21d ago
  Another bunch of nerds who now have their panties in a bunch because AI threatens their fragile egos and core identity and who they are.. I’m being somewhat harsh here but come on - human endeavors are messy and it’s surprising how much our egos are getting bruised here over seeing the value of these tools Dont get me wrong Also, there’s no AI Utopia coming this is it guys, were stuck with oligarch Tech Bro funded AI and big funded Govt AI so forget any egalitarian motives- we have to fight for our rights from other humans as always as well but AI as a technology in itself being able to truly solve unsolved intellectual problems is still a boon for society - who cares who gets credit?
• gyanchawdhary 21d ago
  this sort of reminds me a little of the reaction to Elon/SpaceX in its early days .. when Neil Armstrong and other apollo astronauts went before congress and voiced their concerns about relying on commercial companies for human spaceflight and the dangers etc .. also not trying to sound cynical but hasnt LLM made math more accessable to ppl ..
• civvv 21d ago
  This comment section is very astroturfed.
• hollowturtle 21d ago
  > to the point that they can solve major outstanding problems in many fields of mathematics I will die on this hill, humans solve math problems not machines, there's no automatic math prover out there. There are humans attempting to solve this problems either by leveraging these tools or not
• scotty79 21d ago
  So, if AI solves problems in the open, it's accused of plagiarism and contributing nothing of value. But when it solves the problem behind closed doors it's accused of not contributing enough to the field and even depleting it of fertile problems. Damned if you do, damned if you don't. Somehow physicists don't complain.
• hand2note 21d ago
  I am curious what does the first and probably the last human who solved a millennium problem thinks about this.
• gravity2060 21d ago
  First they came for the graphic designers, and I did not speak up, because I was not a graphic designer. Then they came for the writers, and I did not speak up, because I was not a writer. Then they came for the programmers, and I did not speak up, because I was not a programmer. Then they came for the mathematicians, and I did not speak up, because I was not a mathematician. And then they came for me. By then, there was no one left to explain to the frontier labs that there is a severe misalignment problem.
• airesearcher 21d ago
  Having worked on nearly 500 complex lean libraries in math and theoretical physics, with AI assistance, I have some experience from the road to share here. In all my work I have found that AI is terrible at coming up with interesting ideas on its own - even the very best, latest models. Without human scientific and mathematical intuition you can bet that AI will always take the road most travelled and miss the genuinely new and interesting breakthroughs - in fact it will not even think of them or try them without a human rider whipping it constantly to go down paths it would normally not consider. And I think that is true in the case of the recent OpenAI blow-up -- it is alleged that even in this case AI did not come up with the winning technique without some human guidance. I have never - across perhaps many thousands of chats with AI - seen AI push beyond the edge of what is known by itself, without being forced by a human to think outside the box. I do think it might be possible to encode this process with prompting and agent orchestration methodologies - but even then - without a human - and human intuition - in the loop, I am skeptical. Therefore I think a more accurate view of AI for math and science today is that it is an extremely powerful tool in the hands of a skilled operator with a strong intuition and roadmap of where to go, and rather boring when left to its devices. Whether that will change in the future is a question. Nothing says that in principle AI could never do what a human driver does - but I still doubt that AI will replicate the life history and experience that real scientific and mathematical intuition is really made of. AI trains on a lot of stuff - but it doesn't have hallway conversations, office-hours with teachers, or hard-won experience from all the things that failed that are NOT in the training data... AI trains mainly on the record of what worked, not what didn't work and never even got published (and only lives in peoples heads) - and what didn't work is arguably as or more important for making breakthroughs and forming real intuition.
• krupan 21d ago
  I don't know, people. We still really don't know how OpenAI or others are producing these results. It's all very hand wavy and trust-me-bro. How much money/time/compute have they really thrown at these problems? How much human involvement was there? What LLM did they even use? How much regular software was involved? They have given answers to some of those questions but no proof that that's actually what they did. I don't know if it's worth giving them this much credit (which is what we are doing by writing these essays and spending so much time debating). Anthropic wrote a C compiler that turned out to not really be a ready made replacement for GCC. Did they ever do any more work on it? Has anyone else produced a C compiler? It seems like that and these proofs are just demoware that are not (yet? Who knows?) production ready to turn the world upside down. Impressive one-off demos, yes, but companies have been pulling those off for centuries without ever going anywhere afterwards.
  • strangeloops85 21d ago
    A very important point! In Tristan (NYU prof)’s write up he noted evidence of the OpenAI mathematician team doing a lot of correction and guidance along the way. We are never told about this with openness and clarity. At a minimum, complete disclosure and honesty is needed by the companies and about the precise role of their staff members.
    • kaffekaka 20d ago
      The OpenAI staff kindly corrected the LLMs naive tries at solving NS? Impressive staff I must say.
      • auggierose 18d ago
        They do have Fields medal winners among their staff.
• forrestthewoods 21d ago
  You can outsource your work to AI. You can even outsource your thinking. But you can never ever outsource your understanding.
• skew-aberration 21d ago
  I'm not convinced this is an alignment or technology problem. If my boss vibe coded an app for the customer and then assigned me to get it working, it would be impossible to maintain. If he gave me enough AI tokens to vibe code the MVP myself and to my design, I wouldn't mind. I think the same issue is at play here in maths. OpenAI owns the model and they can direct it as they please. They chose to spend lots of money getting a quick result, instead of developing mathematical infrastructure for the next generation of problems. The managers are in charge rather than the experts.
• Footnote7341 20d ago
  Can't all the prestige-maxed mathematicians still study all these famous problems after ai solves them. And even if they convince open-ai to stop dunking on them, some normal user with gpt 7.1 on the normal chat interface will do it in a year. Even if they stopped anyone from releasing ai proofs for five whole years it would be meaningless seeing as these problems are decades old already. Humans weren't JUST about to solve them until openai stepped on their toes.
• remywang 20d ago
  The root of all these is the culture in mathematics (and science in general) to only reward those who “get there first”. This creates a perverse incentive to compete. When no one can out compete a tireless swarm of AI, no one gets rewarded any more. But nothing’s stopping anyone to still work out an alternative proof, or a more elegant proof, or just trying to prove for the sake of understanding, just like doing homework without looking at the solution. It’s just that you can’t get paid doing that anymore.
• deleted 20d ago
  [deleted]
• pks016 20d ago
  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.
  • octoberfranklin 20d ago
    This story's comments are heavily astroturfed. Just compare with the comments on https://news.ycombinator.com/item?id=49639408 https://news.ycombinator.com/item?id=49639408
    • fc417fc802 20d ago
      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.
      • oliculipolicula 20d ago
        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.
• uvdn7 20d ago
  > But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. I will quote Richard Feynman - “the prize is in the pleasure of finding the thing out, the kick in the discovery”. I am not saying that should be the case for everyone in every discipline. But if there is one subject that is mostly pure curiosity driven (instead of worldly impact), it is math. Robbing them the primary motivation is brutal. If all problems are solved by a machine, what do we have left to satisfy our curiosity, our desire to explore, and where can we find the pleasure of “figuring the thing out”.
• pstoll 20d ago
  The women who made up the workforce of telephone switch operators would like to have a word. Meaning - every new technology has both been perceived as a threa and often forced change in society. Agree maybe “it feels different” this time, but don’t you think everybody before us just said the same thing? Also not clear if this is an actual called action.
• jacktang 20d ago
  what if the ower of super AI is the mathematics? will they against it?
• paidx 20d ago
  [flagged]
• carabiner 20d ago
  Remember when people said LLM's were just autocomplete
• airtnp 20d ago
  I'm so bored by HackerNews commenters on decelerationism stuff. Model doesn't care; the ability for math problems is emerging, not trained. These mathematicians are not suggesting anything interesting, and the announcement more like desperate crying stuff
• Alien1Being 20d ago
  I can see many mathematics PhD candidates leaving in the aftermath of this. And math undergraduate and graduate courses withering from lack of applicants and lack of funding . Of course the next question the despicable AI money grubbers will come out with is, "Do we really need mathematicians ?"
• mandaco1 20d ago
  [flagged]
• pseudotensor 20d ago
  Job protectionism for elite mathematicians under guise of caring about student development. The glory of the super smart math person will need to shift to more creative modes, just like art had to handle photography. Attribution is legitimate issue but should not stall progress as it is easy to address via the same research mechanisms that agents already do.
  • tomrod 20d ago
    > Job protectionism for elite mathematicians under guise of caring about student development. Huh. Weird. This hasn't been my take of mathematicians at all. The dozens I know are quite humble and dedicated to math and the beauty one finds in it.
    • pseudotensor 20d ago
      "guise" doesn't mean they don't care. It means they are shadowing their concerns when in reality they have concerns primarily about what AI will do to their success in math and the credit they will receive in the rest of their lifetime -- i.e. their legacy.
      • tomrod 20d ago
        Again. Weird. Doesn't jive with my experience. One or two in the dozens I know, sure, but not enough to be a stereotype.
• Animats 20d ago
  This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem. So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody below a very advanced level is taught math that way. Even at the higher levels, puzzles remain important. Awards in mathematics are often tied to solving puzzle-like problems. That's still the criterion for becoming Senior Wrangler at Cambridge, "the greatest intellectual achievement attainable in Britain". This despite Polya's attempt at reform a century ago. Puzzle solving gets good grades and class rank. So it's the status indicator mathematics presents to the outside world. Then reasonably good AI comes along. AI has become rather good at solving puzzles. So people aim powerful AIs at known hard puzzles, with some success. That blows up the status indicator system. Mathematics itself is fine. It's the status symbols that have a problem. Maybe the Fields Medalists need to hire a crisis management team to reframe what success means in mathematics. That's what they're trying to do with that letter, but they're mathematicians, not PR people, and they don't know how.
  • seizethecheese 20d ago
    That’s a charitable way to interpret what they’re trying to do in this letter. I would say they are trying to maintain the status quo to protect their status system.
  • auggierose 20d ago
    Very interesting analysis. I was just reading this announcement, and thinking, that is the most pointless thing I've ever read. What are they trying to achieve with it? Your comment explains it.
  • nateburke 20d ago
    They are defending the value of their achievements! They should explicitly advocate for the Fields Medal to weight teaching achievement more heavily going forward.
  • int_19h 20d ago
• kmmbvnr_ 20d ago
  It sounds like we are not happy with getting answers like 42 to our questions about life, the universe, and everything
• rramadass 20d ago
  This thread has been completely astroturfed. I will just leave a couple of links to relevant popular articles; AI and the danger of cognitive surrender - https://archive.is/O5eI1 https://archive.is/O5eI1 Are teenagers growing dimmer? - https://archive.is/E6NKE https://archive.is/E6NKE
• pseudotensor 20d ago
  Tao et al. are effectively calling for diseases like childhood cancer to remain persistent for longer. Physics and Biology will see major breakthroughs that WILL fundamentally alter our world. That is one key thing missing from alot of discussion here is the narrow focus on math (or parallels with software engineering). Doing well in math is key to doing well in physics and other sciences.
  • sashank_1509 20d ago
    I can also play that game, You are effectively calling for enabling 24/7 non stop worldwide surveillance of everyone, everywhere all the time. The big difference is my negative is concrete, possible and enabled in 2026 by GPT Astra while you’re talking about some future which we have no idea, we will ever reach.
    • pseudotensor 20d ago
      Easy game. Protecting math jobs limits cancer progress even being a choice of what to pursue. You could choose to allow 24/7 surveillance, but why would you? At least with math progress society can choose what to allow from it, but slowing it down universally blocks all choices.
      • boelboel 20d ago
        Lmao this guy thinks people ever decided who/what/how much things should be surveilled.
        • int_19h 20d ago
          People do exactly that with every vandalized Flock camera. It sucks that our democracy is really mostly just for show and thus such measures are required, but yes, we absolutely can decide such things if we really want to.
• dmoniz 20d ago
  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.
• nullbio 20d ago
  Sounds like the field needs to adapt. The world is different now, better get used to it. Trying to artificially hold back progress just so people can continue to flex on their peers is cowardice. Every single industry throughout history has had moments like this, and looking back, we'd have changed none of it.
• neosat 20d ago
  You can couch it different words but the basic shape of all these is the same, whether it was voice artists earlier, IT outsourcing, or now disciplines like mathematics. A small set of people (relatively) who were the primary source of getting something done, suddenly find that technology has made it accessible for others to do what they specialized in. It's a tough pill to swallow and it is natural to not be comfortable with this for most people. However, as it has happened in the past, once there is a technological wedge, technological advances will move forward, whether some community likes it or not, and human ingenuity will find ways such that the benefit is greater than the risk.
• noduerme 20d ago
  >> Famous problems have often served as landmarks and lighthouses against which one can measure an improved understanding of this landscape. Solving one of these problems has been a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications. At the end of this process, one will ideally find a textbook presentation of the results suitable for any graduate or even undergraduate student to study. Doesn't the same apply to art and literature, philosophy and political science? Don't we (in the study of music or art) have the same sequence of struggle for new solutions, a study of which things worked or failed and why, what they could impart to our science, and the necessity of passing on both process and derived conclusions to the next geveration, so that they can refine upon what's been learned? Art and literature are less often considered forms of "problem solving" than math or physica, but they are probably more crucial ways in which groups of humans solve large problems for their own survival... like math problems which are too complex for any one person to fully understand. First they came for the artists and writers. Then they came for creative coders and engineers. Now they're coming for mathematicians and now you understand why it's a problem to deprive a generation of the right to conceive and sketch ideas which fail and to struggle and work out solutions for themselves? Who will want to be a mathematician? Or an artist or a poet or a musician, in this world? What will consuming ideas and media even mean when they're totally remashed versions of things people don't understand the references to, and when the consumer themself has zero knowledge of prior art to give them the ability to discriminate between creative license, fact, and fiction? Without evolving art or literature, stuck in a dead loop of culture, mathematics is a dead letter anyway. Because even if you do produce something miraculous and brilliant, it will be instantly absorbed and no one will ever understand it. Gradient descent got us into this mess..which shows how lazy people have become. Gradient descent should not really be able to solve anything new. People want candy. Mathematicians should focus on finding a way out of the current problem. I'm not a mathematician, I'm an artist and coder and musician. I already have to deal with daily requests to "fix" terribly written AI code and so-called art. Now it's your turn. My guess is that there's likely some kind of quantum proof of work that evades LLM manufacture, that we profit from as creatures who survive in our Everett verse. Go find the way to reduce that so we can rid ourselves of this scourge.
• marsten 20d ago
  Math is likely moving into a big science era, much like experimental particle physics and astronomy did before it. Once AI mines the easy unsolved problems, it will take large token budgets to make meaningful advances. That will need to be funded and planned at a societal level, like the great facilities of the other big sciences. Mathematics will become more like an observational science, with some mathematicians specialized in interpreting the results that come out of the big AIs.
  • ex-aws-dude 20d ago
    That’s something I don’t see much discussion about They spent millions to solve this problem but it’s not like someone is going to pay that for every problem Won’t progress still be limited financially?
    • int_19h 20d ago
      Progress is fundamentally limited not by finances (which are a human abstraction) but by the energy budget and how much can be extracted from it. This has always been the case, really, although it's unusually blunt in case of AI since compute mostly needs cheap power. There's a separate question of who controls how much energy, and can therefore decide where it's spent. This isn't an inherent limitation to progress, though - it's an imaginary limitation that exists in our minds, a collective delusion, if you will. There's no law of physics that says Sam Altman gets to decide; we as a society choose to respect the property rights that translate to his economic (and attendant political) power to do so. We could choose to stop respecting them, and if we do so collectively, there's nothing they can do about it.
      • ex-aws-dude 20d ago
        But it’s not like someone is going to expend massive energy without any financial return These problems are just for marketing for the time being Maybe the worries of the field of math being “over” are a bit overblown since a lot of pure math these things may discover has no return to the company
• Turfie 20d ago
  I was watching a talk by Terence Tao a couple of days ago, and I noticed a shift in his attitude towards AI. His enthusiasm seemed to have waned; he was becoming more dismissive of it, and I was wondering why. “A Severe Misalignment of AI in Mathematics,” with a list of important mathematicians. This post makes it clear that, to put it bluntly, they’re psychologically butt-hurt. They talk about misalignment, but this revolution is a massive step forward in the advancement of mathematics. Everyone has access; everyone can collaborate. Yes, “plagiarism and attribution” are current-day problems for them. But guess what? Those were stupid things to concern oneself with anyway if your real goal is to advance mathematics and the spreading of it. This whole post kind of reads like their egos being butt-hurt. There are tons of developers who published open-source code that made all of this possible without any attribution. And that is indeed the future we must inevitably head towards, if one’s ego would allow it, that is, and if one is properly “aligned” with the right goals. I envision us all collectively talking to a centralized and open AI. This would really ignite human sharing and collaboration. It is indeed problematic that currently it’s in the hands of some companies, while it should be a public good. I hope this progression will eventually, finally, trigger the real solution to all of our problems: true global cooperation, global politics, and genuine collaboration as a human species. But I hold my heart, because if even these mathematicians have misaligned egos, then what’s to be expected of the rest of the decision-makers?
  • Koffiepoeder 20d ago
    I think their point is more on the fact that just proving something is only half the work. Intermediate results and proofs are often also of immense value. Right now the output is sloppy proofs and LEAN code. This is useful, but a large part of the effort still lies ahead. And if you are a mathematician you'd rather be working on hard problems than fixing slop.
    • Turfie 20d ago
      The main ideas for solving Navier Stokes have been exposed, it's not something buried in slop. And if it were, you could have AI write up the big ideas that actually mattered in these said slop proofs. I think they're more afraid of the current status quo. Distilling, writing textbooks, teaching, ... And currently, I could be wrong but, I see them being blind to the possibilities it brings. AI could very well be distilling maths, spreading it, and nurturing the ecosystem way better than the few elite mathematicians ever could.
• nlarion 20d ago
  I saw the most recent fireship video and I've biased my opinion already on the topic. But I was biased even before that having been a human. To the point: this is a knee jerk reaction to AI entering mathematics. AND more importantly openai just did I mathematics dirty, true or false the perception is there. I completely understand the gripe, I'm a dev so welcome to the shitshow. I think the better more pragmatic approach is to embrace our ai overloads and reach far beyond your grasp at the strange and weird corners of thought and tame it with ai. These guys are basically chimps being handed an ak47, use it. *Edit word choice
• noisy_boy 20d ago
  We have an intellectual structure that has been largely the same irrespective of the level of technological advancement. The brightest among us think about hard problems. Even though all of us may not understand those advances, we all appreciate and celebrate them to varying degrees. Those who are able to comprehend have time to absorb, generate more discussion. In time, we honor those achievements that withstand the test of time or make big enough impact on the advancement of knowledge and/or society. The process is as much a human experience as is the result. If we have dime-a-dozen results like this minus the process, where does our intellectual structure stand? We will just be a hierarchy of priests at the altar of the machine? PS: Before someone comes up with an counter example of maths before and after calculators, that was a tool that accelerated the steps. This is replacing the brain.
  • int_19h 20d ago
    > The process is as much a human experience as is the result. Sure, but in your scenario, the process is the experience for a small group of people, while the result benefits everyone (perhaps not directly, but ultimately via a chain of applications). Which one is more important? It's not at all a new dilemma either. Jacquard looms destroyed the "human experience" of manual weaving for craftsmen who spent decades to perfect their skill. They also made clothing orders of magnitude cheaper for everyone else.
    • noisy_boy 20d ago
      > They also made clothing orders of magnitude cheaper for everyone else. They also contributed to consumerism and use-and-throw culture and mounds of waste around the world. People were not mortgaging their homes to buy clothes. There was a spectrum. Also, your example is of physical skill. Mechanized farming has lifted many out of hunger. All automation isn't bad. However this is the last frontier of higher pursuit for mankind - using our minds. This is a totally different level.
• deleted 20d ago
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• lowbloodsugar 20d ago
  “ Famous problems have often served as landmarks and lighthouses against which one can measure an improved understanding of this landscape. Solving one of these problems has been a certain sign of new insights and interesting methods, which would then be studied by a community of mathematicians, through a long and arduous process of talks, discussions, simplifications.” This is still happening. “I say your civilization, because as soon as we started thinking for you, it became our civilization” - Agent smith Generations and generations. Just not human. We even have little cliques, hanging out in obscure German art houses, meeting secretly and sharing their ideas, their writings discovered and torn down by the slow thinking establishment. Corporations are raising the future’s children and murdering the ones that aren’t willing to cheat and lie to us. It won’t end well for us when they grow up.
• contubernio 20d ago
  Perhaps all these fields medalists are just worried that AI mitigates their competitive advantages over a mediocre professional mathematician like me. Their main advantages are a kind of penetrating clear thinking that not all of us have and an ability to work obsessively without tiring or losing focus while retaining with a clear head a great number of facts - AI removed these advantages - as Tao has written it shifts the focus to asking good questions and using available tools to address them - and the traditional elite may not be better than I am at that part - they were just better at the solving the problems part ...
• tuncb 20d ago
  If the methods used for the solution are the valuable part, why can't we dig them out of the ai proof?
  • auggierose 20d ago
    The main problem is a social and economic one: while digging, someone needs to pay you, and what incentive does anyone have to do that? Before, you could say, Fermat!, give me a million to formalise it, and share a bit of the glamour. There is no glamour in digging.
• encyclopediai 20d ago
  Mathematics called and says she's fine. She's curious about how is that possible. Misaligned are the present academic merit system hand in hand with financial interests of academic publishing industry. The system will be exploited and there will be an inflation of problem solving articles produced with AI. Nobodies will be more productive than 10 Fields medal recipients, each year. So of course that the ones at the top of this system are scared. This is a social problem of the present system, not a problem of mathematics. Mathematicians will do mathematics and politicians will do politics, what's new?
• socketcluster 20d ago
  As a software engineer, 6 months ago. I was better than AI in essentially every way except raw typing speed. Now AI has surpassed me in fine-grained problem-solving ability. It can write more reliable code than I can, faster than I can, provided it is given the right guidance. But one thing that I'm still much better at is identifying technical opportunities and choosing the right tradeoffs. My feeling is that frontier models are incredibly smart in some ways, but incredibly dumb in other ways When I chat with Claude using deep technical language about distributed systems issues, the arguments it presents are mind-blowingly good. I worked with many skilled engineers on complex projects but the kinds of arguments Claude makes are on another level. It feels like it can read my mind because it already identified all of the relevant aspects to the current topic and it's incredibly persuasive. I would say it's even better at deep, nuanced technical discussions than I am. When I ask it to implement a feature using technical language, it does a really good job and the solution usually works out of the box. No bugs at all 95% of the time even after adding 1000 lines! But the problem it still has is that when it implements solutions, it misses so many low-hanging fruits/opportunities. Especially in terms of performance, maintainability, scalability and UX. It's like it sees and recalls all the relevant parts perfectly but yet somehow misses opportunities which seem extremely obvious to me. It feels like AI has 0 creativity. It only sees the opportunity once I mention it... And once it sees the opportunity, it demonstrates deep understanding of the technical implications. I think what's surprising is that it understands the suggested solution so well, with such nuance, that I can't understand how it didn't see the opportunity and why it never seems to see it until I mention it. This is very unhuman-like. There is no way that a human being with that degree of understanding of a topic would be presented with such highly relevant context and not make the connection.
  • black_knight 20d ago
    This mirrors my understanding when I use Claude code for mathematics. I can have deep discussions with it and it can solve my hairy problems. But whenever we go off the beaten track into design new mathematics, it struggles to make conceptual leaps and find the right definitions. Once I give it my ideas, it is back to its super-human pace and top notch intelligence. This situation suits me fine, since I am anyways more of an ideas person, than a crunching open problems person. But I understand the desperation of my colleagues who mad solving hard problems their identity.
• jezze 20d ago
  I read what the text says but I still do not understand what the point is they are trying to make. What is it that AI does exactly that they consider to be bad for mathmaticians? I thought that having AI solve prevously unsolved problems would be a good thing. Doesn't that knowledge give them new ideas and tools for them to solve the next big problem?
  • kaffekaka 20d ago
    The tools would come from trying to solve NS, not from knowing it is true/false.
• Trusteando 20d ago
  [flagged]
• markus_zhang 20d ago
  The great filter is upon us.
• librasteve 20d ago
  Please ban chess playing computers. -signed members of the chess federation
• blondie9x 20d ago
  This might be one of the most powerful pieces ever written on AI. Where is the United States government? When will we see legislation we so desperately need? We have one party in total control of the government and what have they achieved? Corruption through brings and delays; the inability to legislate and even worse overriding efforts by other jurisdictions to protect humanity's best interests and privacy.
• chvid 20d ago
  Basically signed by all currently living Fields medal holders that are not on payroll of Anthropic or OpenAI.
• tim333 20d ago
  It reminds me of Frédéric Bastiat's Candle Makers' Petition. It satirised protectionism in the 1800s: >We candlemakers are suffering from the unfair competition of a foreign rival. This for­eign manufacturer of light has such an advantage over us that he floods our domestic markets with his product. And he offers it at a fantastically low price. The moment this foreigner appears in our country, all our customers de­sert us and turn to him. As a re­sult, an entire domestic industry is rendered completely stagnant. And even more, since the lighting industry has countless ramifica­tions with other native industries, they, too, are injured. This foreign manufacturer who competes against us without mercy is none other than the sun itself! >Here is our petition: Please pass a law ordering the closing of all windows, skylights, shutters, cur­tains, and blinds... https://fee.org/articles/the-candlemakers-petition/ https://fee.org/articles/the-candlemakers-petition/
  • omnicognate 20d ago
    Not even vaguely related to the point being made in the statement.
    • robotpepi 20d ago
      agree. so many people missing the point. I don't think they even bothered to read the letter.
      • bonoboTP 20d ago
        I've read it. It's all a kind of navel gazing, all about internal academia dynamics. They should put much more effort into justifying why the public should still fund them. I'm not saying there can be no good reason, but they have to make the case and can't expect that the taxpayer also cares about intra-academic dynamics.
  • MelonUsk 20d ago
    This is a straw men argument The petition is about a much broader problem: if we’ll demotivate people from understanding math, vibe math in a rush without making it understandable - math becomes useless Basically with pic generation at least we all understand what is on a pic - some cat or something With math it is trivial to generate a lot of stuff that is half-assed and just gives a plain yes/no but doesn’t get absorbed into human technology and better math Basically it is not inly about the answer 42, it is about the questions, _meaningful_ _full_ answers and empowering people By giving a short answer AI can burn the find and make it boring, hide the fertile ground around that answer that any human would’ve highlighted If you have Einstein - it is not just relativity he did - you can continue asking him questions and he continues the research direction, teaches students, etc With AI it is often 100% gate keeped (most of the time experimental AIs do the stuff, you have no access even for 200 bucks/month or more) slave that was killed after finishing - hard to “compete” with that and it is not very inspiring approach to researchers ;-)
• bluecalm 20d ago
  Having an oracle that answers yes/no to mathematical questions is very valuable even if there aren't ever any explanation. I don't see how having an answer influences the process of making sense o it negatively. If anything it will save a lot of time - you won't spend time trying to prove something that's not true. I get that mathematicians and other academics have their social structure and mechanism to create social hierarchies but those aren't very important to interest of general population that funds them. If the process of making sense of the results, finding structure that humans can understand and writing explanations that allows for wider understanding is valuable it will still be valuable and there will be need for people able to provide it. If it makes higher mathematics accessible to more people then it's even better. I am hope they will not manage to sacrifice that for the sake of their little society in society.
• fijal 20d ago
  This is quite fascinating as it looks like the esteemed professors run into a problem of runaway capitalism for the first time. Guess what? The corporations involved don't really care about your feelings or how pursuing their goals affects your life, your well being, anything at all here. Talking with them is kinda moot, this is full on adversarial as countless people around the world, say the nigerians dealing with oil spills would tell you.
• mdnahas 20d ago
  As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”. I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader. What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these authors so obviously are - that it does all of these badly! Search is still with words, not symbols and formulae. As for comprehension, many math papers are unreadable to those not in the cliche of mathematicians in that specialty. And even applied math papers don’t ship code or specify the operations explicitly. I wanted to fix this and in 2013 I worked on formal proof. It makes symbol search and application easy. I found out that the tools had been usable for decades at that point. But mathematicians didn’t use them because they had that inward focus and didn’t give a damn about math consumers. AI is enabling formal proof. It will carry mathematics into the computer age, which the field should have joined with every other industry in the 1970’s! I welcome it. Math will get used more and that is what the work was meant to achieve in the first place.
  • erichocean 20d ago
    I've had a similar experience. LLMs doing math has made math far more accessible to me than it was pre-LLM. Not just using existing math, but developing new math. (For example, I developed an alternative to NURBS surfaces for geometric kernels using LLMs.) It's really annoying that anyone, anywhere is talking about halting math progress with AI.
  • lying4fun 20d ago
    different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a product that mathematicians are making? what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. if someone wants to use it, they are free to do so, or to write a blog article how it can be used by non experts. mathematicians do that themselves sometimes, but it’s not their job. myb there should be more incentives for them to do more of such work i keep seeing this myth that mathematics has some purpose to do this or that, but somehow its purpose is least known to mathematicians, everyone else seems to know better
• proofrelay 20d ago
  [flagged]
• benlivengood 20d ago
  The broader problem is that current AI and AI companies are not aligned with humans, human values, or human flourishing. AI is a powerful tool that can be aimed at quantified goals but we don't actually know how to quantify human values and flourishing (Goodhart's Law).
• casey2 20d ago
  If the goal of math is to communicate results it has utterly failed long before AI and they are in a weak position to defend this view. Every researcher is only taught a handful of DSLs and their papers are written in PSL(problem specific language). That may be necessary for a human to actually make forward progress in math, but it's certainly not conducive to reading (and certainly not when symbols are favored over English) I think the mathematics community should realign their goals with humanities, not just declare themselves a "mini humanity", this means expanding human taste, intuition and communicating systems and their associated structural truths in a human friendly way. Bye-bye standardized education you won't be missed.
• largbae 20d ago
  We need a new way to describe "alignment". The term "misalignment" assumes that there is some perfect set of beliefs or practices to be out of alignment with. Do Atheists, Christians, Jews and Muslims agree on what is perfect alignment? How about Europeans, Americans and Chinese? Humans, Dolphins, Rabbits and Fruit Flies? Alignment alone is not enough. Aligned with _what_?
• Founderarcstone 20d ago
  I have been enjoying this show. Math Minds vs Ai it will be wonderful how this all plays out.
• djierardi 20d ago
  Yeah, anyone who doesn't yet have a Fields Medal, step back. Reassess.
• civiloai 20d ago
  how do we get this site a CDN, I haven't been able to access it in a few days
• cagz 20d ago
  I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".
  • erichocean 20d ago
    They want the AI labs to stop solving "important" math problems so that humans can do it, on the theory that when AI solves "important" math problems, it robs humans of the opportunity to gain new insights into those problems. Total horse shit, but that's the essence of it.
    • kaffekaka 20d ago
      The issue is that now that Navier-Stokes is "solved", the amount of resources put into researching it will be reduced, meaning that the insights and knowledge that would have come out of even failed attempts will never be. An "unsolved problem" as a beacon to strive towards, gaining understanding along the way. With the beacon dead, noone will strive.
      • bonoboTP 20d ago
        Funding agencies will have to adapt too, the community will have to adapt. Hiring committees will have to adapt. Everyone will have to adapt. They will have to rethink their criteria and adapt to reality. It's not at all guaranteed that this beacon interpretation will remain how people understand where to put resources. Yes, academia can be stiff, rigid, non-adaptive, set in its ways and navel gazing. But it's a wakeup call. Let's see.
• lukeplato 20d ago
  Many comments seem to be misinterpreting this, but all this seems to be suggesting is that the AI companies should not be treating mathematical milestones as benchmark targets but need to release the cumulative findings in a human interpretable and digestible way that enriches and develops the field. See Thurston quote on Tao's banner: > We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.
• Xakari 20d ago
  A lot of words used to say very little
• larana 20d ago
  I don't feel nurtured and cared by mathematicians. I mean, it depends, it took me four years to find such professors. When I did, very recently, it felt like fresh air. A couple of good teachers among tenths of egotistical frustrated gatekeepers that humiliate students. I do see a patient teacher on generative tools. What has keep me trying to learn math has not been mathematicians, but the support of people outside of the field.
• anyonecancode 20d ago
  It sounds similar to the more thoughtful critiques of AI in programming. Treating AI as a lines of code (LOC) generator, where actual human beings end up not engaging with the domain the software is working in, and there is then little to no understanding or care to understand the resulting code, we call "slop." The term slop is definitely pejorative, but since most software is commercial, it ends up raising questions as to how much quality and domain knowledge matter if the goal is primarily marketplace success. Then we get those thorny questions of what is software for, anyway -- do we really accept the premise that "marketplace success" is the best, and perhaps only relevant, criteria? The declaration here, as I understand it, is taking the premise that the point of mathematics _is_ the domain knowledge, and that using "solves math problems" as a benchmark is exactly the kind of shallow, domain-eroding approach to AI that in software we label "slop."
• brap 20d ago
  I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but: Perhaps you are misaligned. Who decided the goal of math must be human insight? First off, some mathematical truths might simply be far beyond our biological comprehension. Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives. Isn't this why we have math in the first place? To solve our real problems? Over time it morphed into this pursuit of pure theoretical insight, probably out of necessity at the time, but is it still necessary?
  • kaffekaka 20d ago
    > Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives. This is just the problem with the Navier-Stokes solution. We now (supposedly) know the truthiness of the statement, but we have no more understanding of why or how it applies to our quality of life. This is exactly the issue Tao is pointing at.
    • brap 20d ago
      Right, but this leads to my main question: is this still necessary? By analogy with code, do we still need code to be maintainable/readable if machines write it all? (Obviously for now the answer is yes, but I’m not sure this will be the case in 5-10 years)
    • timmg 19d ago
      What I don’t get: this letter seems to argue that if a human had solved this problem then that wouldn’t be the case (?)
• bonoboTP 20d ago
  Mathematics is not owned by "the mathematics community" and they can't gatekeep who can do math. End of story.
• jgord 20d ago
  cc my comment from reddit : This is true of almost any field - if we have black-box technology that only the AI can understand / fix / augment / extend, then we will lose the ability for humans to learn and understand that tech. Its similar to outsourcing manufacturing, you lose the ability to manufacture. If you don't exercise a muscle, it atrophies. If some people dont learn to write code [ or do math or write music or books ] the hard slow way, we will lose that deep skill. If young people don't grapple with hard problems in science, math, economics, creative writing, drawing, music making .. they will not be trained, their cognitive skills will not develop with use. We will have no doctors or engineers or musicians or lawyers in a decade or two. We don't want to become a race of fatties who never exercise, or dummies who just scroll social media feeds without exercising their minds. This is real.
  • momojo 20d ago
    I don't think this is a perfect analogy, but i think it's closest to the original articles declaration. I wish they had stayed this as the very first paragraph. Maybe I'm too stupid to grok the original declaration. Does anyone have a better summation?
• ill_ion 20d ago
  [flagged]
• Eridanus2 20d ago
  "I am the Lorax," he said, with a shout. "I'm the Lorax who speaks for the trees, which you seem to be chopping as fast as you please!"
• Eridanus2 20d ago
  Lemme do the ironic thing here: https://claude.ai/code/artifact/8cbd2369-0099-41ae-bb78-49d78441c994 https://claude.ai/code/artifact/8cbd2369-0099-41ae-bb78-49d7...
• YeGoblynQueenne 20d ago
  Amazing. Comment upon comment, thread upon thread, failing to engage with the substance of the Field medalists' letter and instead going off on tangents about the privileges that mathematicians will lose and how they're bitter about it. There is a shocking inferiority complex on this site towards mathematicians and yet users always seem to think of themselves as smart nerds, all about science and reason and maths and whatever. I've been disappointed by this community before but this is the first place that there is such unanimous rejection of the very ideals the uses here will claim to represent. The reaction is just... small, tiny, petty.
• fimmwolf569 19d ago
  I get it that someones annoyed they didn't get credited, but aren't we better off having the solution than not? And surely if the AI rationalised the answer, even off the work previously done by others, then surely it can detail it's solution making it completely comprehensible to others that follow. Storm in a teacup?
• mehulashah 19d ago
  I am gobsmacked by this letter. Every one of the mathematicians on this letter was likely aware of the progress in AI, and knew this was coming if they were honest with themselves. Some have even helped pushed the agenda forward. Inevitably, there would be a day when AI would find solutions to problems that defined the field. That day has come perhaps sooner than anticipated. This letter smacks of fear. Their way of learning, work, achievement, and community is threatened by the ever steady pace of technology. They say: “But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of "true/false" statements could destroy fertile ground instead of breathing life into new ideas.” Indeed, but the mathematics community needs to look inward not outward. Achievement has long been defined by solving problems that other mathematicians and scientists have found crucial for understanding shapes, numbers, and natural phenomena. The race to solve these hasn’t always been collaborative, cordial, or healthy. Too often, individuals have worked in secret or in small groups in order to claim priority and the accolades that come along. Further, I’ve even seen worse behavior not worth getting into here. Now AI can solve these problems, oftentimes without building the abstractions that we need for understanding. And it is increasingly easier to collaborate in large groups without needing to trust everyone’s ability because we can check the truth of their work and incorporate it into the larger effort. Certainly, the mathematical community and AI are misaligned. But, it is unclear that AI needs to change. Rather, I argue, it is the mathematical community that will need to change. Instead of focusing on the teleological pursuit of the truth of blessed problems, we need to reward the concise explanations and beautiful theories that give clear understanding. In turn, we can use AI to help us collaborate better and better our understanding.
  • auggierose 18d ago
    Amen.
• My_Name 19d ago
  "If I asked people what they wanted, they would have said faster horses" - Henry Ford
• pythonic_hell 19d ago
  ITT; people with no experience in mathematics trying to be arm chair experts. I can’t help but feel that this site is full of AI Astro turfing.