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Responsible Release of AI-Generated Mathematics

123 points · 223 comments · aureianimus

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  1. aabhay · · focus · HN ↗
    I don’t understand the argument. What if OpenAI doesn’t have anyone that actually fully truly understands and wants to take responsibility for the findings? Like many things, verifying a solution is often much harder than explaining why it’s correct. If this were the standard then it would seem to support the company withholding release, in order to find someone who can spend weeks examining and articulating the solution.

    Be careful what you ask from people, because they might do what you say.

  2. throwaway713 · · focus · HN ↗
    > we ask them to stop testing advanced mathematical problems on proprietary models.

    Maybe I'm alone on this, but for some reason these sorts of requests strike me as akin to gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop.

    Ensuring credit where credit is due? That's fine. If your model incorporates the efforts of many others, then it's reasonable to request acknowledgement of everyone who contributed (even indirectly). But that's not what the request states — presumably their ask subsumes any advanced ML model, including those that weren't trained on a giant corpus of text.

    1. Davidzheng · · focus · HN ↗
      You're not alone, even among mathematicians.
    2. mmaunder · · focus · HN ↗
      Humans have been trying to outlaw thinking for some time now.
      1. xanderlewis · · focus · HN ↗
        What (some) mathematicians are asking for, whether one agrees with it or not, is exactly the opposite of 'outlawing thinking'.
      2. GPerson · · focus · HN ↗
        Presumably this refers to the cognitive surrender most of HN is celebrating the arrival of?
    3. Joker_vD · · focus · HN ↗
      > gatekeeping how someone should breathe air. It's math... the numbers and symbols are just out there in the platonic realm available for anyone to do as they like with them. It's patently absurd to request other people to stop.

      The chemical compounds of all kinds are also out there, available for anyone to do as they like with them. Say, mixing ammonium chlorate with peroxide, why not? Or potassium permanganate with powdered aluminum. It's patently absurd to request other people to stop.

      1. pfisch · · focus · HN ↗
        It's illegal to make weapons out of chemicals because the government has a monopoly on violence.

        Mix together whatever you want, and then you can fight the feds when they show up to enforce their monopoly.

      2. mathisfun123 · · focus · HN ↗
        > The chemical compounds of all kinds are also out there,

        1. Lol but they're literally not

        2. A sample of chemical compound and a piece of math don't share literally any ontological qualities - you might as well have tried to make a comparison between math and nude pictures of the President

        1. Joker_vD · · focus · HN ↗
          They literally are though.

          > you might as well have tried to make a comparison between math and nude pictures of the President.

          The latter is but a very large number, interpreted in a particular way. Have you heard of "illegal numbers"? Yeah, apparently they exist. That damn state, treading on literally everything that humans might do as if it's any of its business.

          1. bananaflag · · focus · HN ↗
            Link for curious people

            <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Illegal_number" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Illegal_number

    4. omnicognate · · focus · HN ↗
      &gt; gatekeeping how someone should breathe air

      Air is there for all to breathe. It&#x27;s a more-or-less fungible, free resource for all to use and the consumption of it is a basic requirement for life.

      The AI companies, in contrast are using vast financial, human and compute resources to train and operate specialised models that are not available to the public. The advisory group&#x27;s job is to give non-binding advice on how they can use this privately owned technology in a responsible manner that avoids doing unnecessary harm to the mathematical community. To call that gatekeeping misses the point entirely.

      1. dr_dshiv · · focus · HN ↗
        The AI models are most definitely available to the public with a maximum of what, a 3 month lead while they do testing?
        1. omnicognate · · focus · HN ↗
          The very first paragraph of the article says (emphasis mine):

          &gt; At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. Our recommendations are formulated with this practical context in mind.

          The Navier Stokes proof came from an internal model that AFAIK still has not been released even in a limited way to scientists, let alone to the general public. Publicly available models are not what these mathematicians are talking about.

        2. eli_gottlieb · · focus · HN ↗
          Air is both free as in beer and free as in freedom. Proprietary language models are neither.
          1. hardbass · · focus · HN ↗
            Why are you confusing the substance&#x2F;field with the tools to use it? He said air is free which is correct. You and parent are complaining that air compressors cost money and are proprietary.
        3. GPerson · · focus · HN ↗
          This is an extremely privileged take. Most of the world cannot spend thousands of dollars a year on this.
      2. psychoslave · · focus · HN ↗
        Air is not impossible to disrupt in quality as side effect of industrial hubris.
      3. hardbass · · focus · HN ↗
        Air is for everyone. Nobody stops you from buying or making a 1hp compressor or an ai company owning a 10hp compressor.
    5. knuckleheads · · focus · HN ↗
      I don&#x27;t see why mathematicians should be protected from AI anymore than any other profession. It&#x27;s either everybody or nobody, not fair on the face of it otherwise.
      1. aprilthird2021 · · focus · HN ↗
        Mathematician was never really a &quot;profession&quot; like the others. It doesn&#x27;t pay well and is largely confined to academia. If you&#x27;re really good and want to get paid, you don&#x27;t do the kinds of problems AI have been taking a crack at. You go to a quant firm or some tech company where this kinda math actually matters once in a blue moon
      2. seanhunter · · focus · HN ↗
        TFA isn&#x27;t asking for mathematicians to be protected from AI. It&#x27;s asking AI labs to hold themselves to the standards of the mathematical community:

        - releasing papers using the normal process to allow peer review

        - giving talks etc to disseminate knowledge so humans understand the result

        - writing papers in a way (standard terminology etc) that allows mathematicians to digest the result (some AI math papers comprise a huge verbose load of non-standard terminology and waffle and then a massive lean proof. This is very hard for humans to actually understand, and means it&#x27;s hard for others to take the work forward.)

        - giving appropriate credit to results that are used to derive the work

        It includes some specific recommendations for situations where the person prompting the model is not in a position to understand the output, and frankly these are really welcome given situations like the recent case at Anthropic where a non-mathematician at Anthropic prompted claude to make a significant improvement to the bounds of a problem related to the Riemann Zeta function[1] which led to widespread misreporting and claims (not by Anthropic themselves notably) that the Riemann hypothesis itself had been proved, which is emphatically not the case.

        Research mathematics is fundamentally a collaborative activity and the way in which some of these results are released is done to maximise PR but means a ton of the mathematical value is left on the table.

        [1] <a href="https:&#x2F;&#x2F;www.anthropic.com&#x2F;research&#x2F;riemann-zeta" rel="nofollow">https:&#x2F;&#x2F;www.anthropic.com&#x2F;research&#x2F;riemann-zeta. As I understand it, the Riemann Hypothesis says that all non-trivial zeroes of the zeta function lie on a line called the critical line. Two centuries of previous work had established that at least something like 40.9% of the zeroes lie on the line and noone has ever found a non-trivial zero that does not lie on that line. Claude (with prompting from a non-mathematician to &quot;try harder&quot; etc) improved this bound massively to 67%. Now a lot of people said things like &quot;OK so all we&#x27;ve got to do is to improve that to 100% and we&#x27;ve proved the RH&quot;, which is definitely not true unfortunately, because you can say that in the limit the proportion of the zeroes on the line is 100% and still have infinitely many which are not.

        1. knuckleheads · · focus · HN ↗
          Maintaining the existing standards is in fact a form of protection from AI disruption. They are asking the AI companies to follow their norms, instead of them having to conform to new norms created by AI. They don’t want to have to change the way they do things, understandably!, and are asking the companies to accommodate their way of life.
          1. curt15 · · focus · HN ↗
            New norms are only worth adopting if they are clearly better, and that is far from obvious for whatever norms the proprietary AI companies are trying to push. Also their letter specifically targets proprietary AI companies, not computational tools in general which mathematicians do use when they advance mathematical understanding.
            1. knuckleheads · · focus · HN ↗
              Better for who? If I don’t care about the welfare of mathematicians and just the advancement of mathematics, would AI doing the math not be better for me?

              As well, if the open models were as good as the proprietary ones, do you think they wouldn’t still have complaints?

        2. munksbeer · · focus · HN ↗
          Those seem reasonable apart from this one:

          &gt; - releasing papers using the normal process to allow peer review

          I&#x27;m not an academic but I&#x27;ve heard enough stories about how this can very much act as gatekeeping that I don&#x27;t think it is a good request.

          1. GPerson · · focus · HN ↗
            Is “gate keeping” a new toy for ai bros or something? Peer review has a purpose… You guys should try to understand systems before you celebrate their death.
            1. munksbeer · · focus · HN ↗
              I freely admit I am not an academic. I just note that there is a lot of negative sentiment about people trying to get stuff published, and a lot of it looks from an external perspective to be elitist gatekeeping.

              Please read that again, I am not on the inside here, so anything I say is just based on reading stuff from aspiring academics and articles in that mode. To my amateur eyes, there seems to be a problem in the academic world, of some sort, but how big it is, or isn&#x27;t, I don&#x27;t know.

              Is that ok?

              So, assume I, a complete amateur, no PhD, no connections or academic record to speak of (I have an MSc only, from the 90s, in a third world country) thinks I&#x27;ve discovered something, how do I go about &quot;publishing&quot;?

              To me, I could easily see value where I self publish somewhere, where other similar non-connected people can see, crowd source the verification (basically peer review) and if it turns out to be useful, it&#x27;ll be used.

              Maybe it would be easy for me to get it formally published, but I doubt it.

              1. GPerson · · focus · HN ↗
                First of all if you think you had discovered something in a pre-AI world, there’s a 99% chance it’s some triviality or wrong. Mathematics is extremely rich and people spend their entire lives thinking about it. Undergrads can’t comprehend what the grad students are studying. Grad students can’t comprehend what the post docs are doing. And it just goes and goes.

                In a post-AI world there’s a mountain of high quality work being published by people who actually know what’s going on. You can probably make a discovery with chatgpt right now, but why should someone who’s got a ton of things to do already read your article? You’re free to put it online, but why should you be free to force someone to read something?

                1. munksbeer · · focus · HN ↗
                  &gt;In a post-AI world there’s a mountain of high quality work being published by people who actually know what’s going on. You can probably make a discovery with chatgpt right now, but why should someone who’s got a ton of things to do already read your article? You’re free to put it online, but why should you be free to force someone to read something?

                  But aren&#x27;t you literally just proving what I&#x27;m saying? The original argument was that everyone should have to post through peer reviewed journals, I said that is probably gatekeeping too far, and your response above just confirms my suspicions.

                  &gt; Second of all, it’s extremely aggravating to read all these software people criticizing mathematicians, who almost universally have low salaries and who chose to go into this profession because they care about contributing to human knowledge.

                  I probably agree with you, except I have never and am not criticising mathematicians. I am only saying that there are quite a lot of reports around that the academic world is fierce and that sometimes there are high barriers to getting something recognised.

                  No idea if it is true or not, but my personal opinion is that it isn&#x27;t going to matter much in the future. If it exists, then people will work around any gatekeeping.

        3. T-A · · focus · HN ↗
          From the opening paragraph:

          we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models

          From point 2 under section &quot;1. Background&quot;:

          AI labs should provide significant support, including funding, to help develop this understanding

          Point 3 under the same section:

          The development of human understanding must remain organic and community led. It should not be directed by AI labs, even when the labs have produced the results.

          If, as you say, they are &quot;asking AI labs to hold themselves to the standards of the mathematical community&quot;, I must conclude that the mathematical community

          1. Ideally wants a monopoly on mathematics research.

          2. Wants those who dare violate their ideal monopoly to fund them.

          3. Insists that the ideal monopoly remain in charge.

          1. dotancohen · · focus · HN ↗
            Math is a tool. It&#x27;s what people do with the tools after they are invented that matters - and with mathematical tools sometimes that wait is hundreds of years.

            The mathematics community has found that the tools have value long after being invented if the inventor leaves his tools in a specific format. The community is doing its best to preserve that - not because they want less toolmakers, but rather because they want the tools to be useful when they become needed.

          2. curt15 · · focus · HN ↗
            Your monopoly theory lacks a credible motive. The group (<a href="https:&#x2F;&#x2F;agmai.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;agmai.org&#x2F;) comprises of world-renowned mathematicians, including several Fields medalists, who no longer have any need to prove themselves or monopolize a field. If they felt like it they could quit mathematics today and find private sector jobs paying far more than their professor salaries.

            The basic purpose of mathematics has always been human understanding:

            &quot;The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat&#x27;s Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.&quot;

            <a href="https:&#x2F;&#x2F;mathoverflow.net&#x2F;a&#x2F;44213" rel="nofollow">https:&#x2F;&#x2F;mathoverflow.net&#x2F;a&#x2F;44213

            1. T-A · · focus · HN ↗
              &gt; Your monopoly theory lacks a credible motive

              The motive is obvious and all over the comments. For you convenience, it can be summarized as gatekeeping. Start unpacking it and you will find ego (these are people at the top of a cloistered social pecking order who suddenly see that order threatened), entitlement (their writing reflects a belief that they own mathematics and have the right to dictate how it&#x27;s done by others) and economics (academic funding follows prestige; being outdone by machines undermines the prestige, hence the funding).

              &gt; and also ignores the fact that your quote specifically targets the frontier labs, not LLMs or computational tools in general

              That&#x27;s like saying &quot;your opposition to autonomous weapons ignores the fact that they specifically target [INSERT FAVORITE TARGET]&quot;. I ignore what&#x27;s irrelevant.

              If Ken Griffin had not chosen to donate $3 billion to CMU [1] and instead had spent that money on tokens to solve a bunch of open problems [2][3] using publicly available LLMs, do you seriously believe their reaction would have been more positive?

              &gt; The group (<a href="https:&#x2F;&#x2F;agmai.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;agmai.org&#x2F;) comprises of world-renowned mathematicians, including several Fields medalists,

              I am well aware of who they are, thank you very much.

              &gt; who have nothing left to prove.

              In the old order now under threat.

              &gt; If they felt like it they could quit mathematics today and take private sector jobs paying far more than their professor salaries.

              A common delusion among students and maybe even some professors who&#x27;ve never set foot outside academia. The authors of TFA know better, of course. Their current conditions amount to enjoying a comfortable living while pursuing their favorite hobby full time. In the private sector they would have to justify their salary by (gasp) working on something (OMG!) applied with a reasonable prospect of (would you believe it?) meaningfully contributing to their employer&#x27;s (pardon my French) bottom line. A revolting thought, and prospective employers know that too. Both parties know it wouldn&#x27;t work.

              &gt; the working group&#x27;s various recommendations simply aim to ensure that computer-generated mathematical activity aligns with that purpose

              If so it completely misses the mark.

              [1] <a href="https:&#x2F;&#x2F;abcnews.com&#x2F;Business&#x2F;wireStory&#x2F;hedge-fund-ceo-ken-griffin-record-3b-carnegie-136881643" rel="nofollow">https:&#x2F;&#x2F;abcnews.com&#x2F;Business&#x2F;wireStory&#x2F;hedge-fund-ceo-ken-gr...

              [2] <a href="https:&#x2F;&#x2F;www.unsolvedmath.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.unsolvedmath.com&#x2F;

              [3] <a href="https:&#x2F;&#x2F;www.openproblemgarden.org&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.openproblemgarden.org&#x2F;

          3. Chance-Device · · focus · HN ↗
            Yes. It’s remarkably flagrant, and it’s an example of an academic mindset that’s likely been holding progress back across multiple fields. It’s about to be broken rather badly, and it will show where progress has been stifled.
          4. shank-false-rin · · focus · HN ↗
            The mathematical community isn&#x27;t really a single entity. It&#x27;s weird to call that a monopoly.

            An (obviously not 1-to-1) analogy is Amazon uses their platform sales data to push out almost identical AmazonBasic branded products. Small businesses can&#x27;t compete, because Amazon has the economy of scale.

            I am not saying that what Amazon doing is &quot;wrong&quot; per se, but I bet if small businesses have a voice they&#x27;d also ask Amazon to stop blatantly coping their most popular products.

            It&#x27;d be weird to say that &quot;the small businesses wants a monopoly on [insert product].&quot;

      3. GPerson · · focus · HN ↗
        This is just absurd.
    6. nxpnsv · · focus · HN ↗
      But on one hand there are labs that pushes tens of millions $ to mine for publicity, and on one hand mostly underfunded researchers trying to improve general understanding. Big ai may seriously harm math and when Pr value diminishes down nobody is there to keep pushing.
      1. dr_dshiv · · focus · HN ↗
        “researchers trying to improve general understanding”

        Pretty sure AI will do better for that.. mathematicians need to be centaurs like the rest of us and stop rhetoric that is going to make existing math centaurs feel like they might get math-cancelled

        1. nxpnsv · · focus · HN ↗
          My point is that there is a real difference between massive ai company budgets and research mathematicians driven it, it is not an argument against use of ai which seems inevitable.
        2. aeve890 · · focus · HN ↗
          &gt;mathematicians need to be centaurs like the rest of us and stop rhetoric that is going to make existing math centaurs feel like they might get math-cancelled

          Centaurs?

          1. peri-cl · · focus · HN ↗
            (An inseparable fusion of two distinct animals, in this case human&#x2F;AI. HN uses the word often where &quot;cyborg&quot; would fit. Also: &quot;reverse centaur&quot;, with the human part lacking a head).
            1. api · · focus · HN ↗
              I prefer thinking of human AI fusion like a lichen, which is a close symbiosis at the cellular level. That’s what it would look like.
          2. hidroto · · focus · HN ↗
            &#x27;centaurs&#x27; is a term from chess, where people play chess with computer assistance.

            <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Advanced_chess" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Advanced_chess

        3. hardbass · · focus · HN ↗
          I believe Alpoge was already a centaur.
        4. GPerson · · focus · HN ↗
          You’re not engaging with anything in reality. Mathematicians are adopting AI. Go read Terence Tao’s blog posts. People like you just invent a fantasy to get angry at.
    7. Chance-Device · · focus · HN ↗
      You’re not alone at all, gatekeeping is exactly what this is and that’s clear from the text almost immediately.
      1. GPerson · · focus · HN ↗
        Next time you make any argument to protect something you find meaningful and important, and something you believe you add value to, just remember it’s pure gate keeping and everyone can see it.
    8. bananaflag · · focus · HN ↗
      Note that they&#x27;re saying &quot;proprietary models&quot;. Probably open models will reach this level in a year or so and then this discussion will be moot.
      1. GPerson · · focus · HN ↗
        I doubt it. You have to make these 1000 times cheaper at the same level as the internal model at OpenAI for random (wealthy) people to start knocking down major conjectures.
    9. skeledrew · · focus · HN ↗
      &gt; requests strike me as akin to gatekeeping

      This is exactly what I was thinking as I read it, along with the bit that AI labs should support human understanding. The whole thing smells as they&#x27;re trying to place this burden on labs that are just offering a tokens service; them publishing about particular topics is essentially a side quest in the first place IMO. If a community wants to create Math labs dedicated to understanding AI discoveries in the field, then they&#x27;re free. If they want to petition AI labs for financial support, they&#x27;re also free. But this wording where they&#x27;re trying to dictate what AI labs should do (outside of their primary business) just smells.

      1. GPerson · · focus · HN ↗
        I’ll never understand why ordinary people would take the side of oligarchy over one of the most humane institutions on the planet.
        1. hardbass · · focus · HN ↗
          To an ordinary person this sounds like, mathematicians were doing something, a team of scientists at OpenAI beat them fair and square in honest conditions and now mathematicians are whining and requesting artificial protections. I am not saying if this is what I believe, I meant this is how it will look from outside.
          1. GPerson · · focus · HN ↗
            To all ordinary people, OpenAI sought these people out and asked for their opinions on how to stop harming the math community.

            Ordinary people just run with whatever two minute understanding propaganda delivers to them and then settle into hard opinions.

    10. curt15 · · focus · HN ↗
      The problem with proprietary models is that you don&#x27;t get to poke inside and see what it is doing and how it arrives at its final answer. Mathematical understanding derives less from any particular result than the insights and methods that pave the road to results. Whenever a theorem is proved, researchers seek to unpack the proof and get inside the author&#x27;s mind to learn their ways of thinking.

      LLM generated results could conceivably advance mathematical understanding if researchers can inspect their intermediate reasoning traces to discover erroneous human biases or patterns that they might have previously overlooked. Otherwise, the results might as well be produced by oracles.

      1. semiquaver · · focus · HN ↗
        &gt; The problem with proprietary models is that you don&#x27;t get to poke inside and see what it is doing and how it arrives at its answer, which is precisely what mathematicians do

        Uh, a hypothetical fully open source model would have the exact same problem, because LLMs rely on emergent phenomena and no one understands why they work.

      2. trhway · · focus · HN ↗
        &gt;Otherwise, the results might as well be produced by oracles.

        no. The math result is a result only when it includes proof. The proof is the value here. The way somebody came to it isn&#x27;t really important - we don&#x27;t know how Newton came to his results, whether it was apple or pear, and it isn&#x27;t really important. Or how Einstein was walking the city streets looking at the tower watches - it is just historic curiosity having no real value for science.

        That has been one of the greatest thing about math departments - smooth talkers were always clearly visible as smooth talkers. You&#x27;re either producing proofs, or you&#x27;re anything but a mathematician.

        I feel for mathematicians. They have similar situation like we have in programming. Well, we all just have to evolve and adjust (in particular reign in our pride as just in a few years - once LLMs start hitting 100T+ - we may loose our &quot;top of God&#x27;s creation&quot; position). Any attempts at gatekeeping, ludditing, organizing in quasi observational&#x2F;advisory boards really intended to protect their tenures, etc. ... - well, you just can&#x27;t stop the wave.

        It all reminds how Catholic Church insisted on responsible release of the Bible in German. The Church even unleashed the devastating 30 Years War trying to protect its monopoly on religion including the right to sell indulgences, etc.

        &gt;AI labs should provide significant support, including funding

        And now all those &quot;responsible math&quot; and advisory boards would like to preserve their monopoly on math and would like to sell the indulgences to the AI labs. As usually it is all about money and power, not about science. As a Math PhD dropout myself i feel a bit of a shame and disappointment for that undignified scramble by the mathematics establishment. Being smart they should have led the way and show an example to the rest of humanity ...

        1. jltsiren · · focus · HN ↗
          When I was a postdoc in genomics, one of my supervisors had a background in mathematics. Current bioinformatics training pipeline didn&#x27;t exist yet, so most PhD students and postdocs had a background in something like CS, mathematics, statistics, or physics.

          From the supervisor&#x27;s perspective, people coming from pure mathematics were good at thinking about definitions. Coming up with useful definitions was the primary value they created, while theorems and proofs were just technical stuff they did to evaluate the value of proposed definitions.

          My own background was in theoretical computer science, specifically algorithms. When you do algorithms without any qualifiers, you are studing them as mathematical objects in a simplified model of computation. The process often starts with a promising algorithmic idea. But if it looks like you can&#x27;t prove anything nontrivial about the idea, you often stop studying it, regardless of the actual value of the idea. And if you manage to prove something, you start optimizing the algorithm for your theoretical model in order to prove better results. That usually makes it worse in practice.

          The end result is that algorithms papers, both good and bad, typically contain theorems and proofs about algorithms nobody cares about. If you are a practicioner, you need to dig through all that noise to find the core algorithmic ideas, so that you can evaluate them in a more realistic setting. And if you are a theoretician, you are probably more interested in the techniques used in the proofs (which may also inspire future algorithmic ideas) than in the actual results.

          You can find plenty of other similar situations. The value mathematicians create is rarely in the theorems and the proofs.

          1. trhway · · focus · HN ↗
            notice that you&#x27;re talking about areas other than mathematics. I was talking about mathematics.
            1. jltsiren · · focus · HN ↗
              I was talking about the value created by mathematics. Which largely comes from training people to think about technical details. Which typically manifests as new ideas based on deep technical understanding of earlier ideas.
        2. curt15 · · focus · HN ↗
          &gt; The math result is a result only when it includes proof. The proof is the value here. The way somebody came to it isn&#x27;t really important - we don&#x27;t know how Newton came to his results, whether it was apple or pear, and it isn&#x27;t really important. Or how Einstein was walking the city streets looking at the tower watches - it is just historic curiosity having no real value for science.

          This mischaracterizes the role of rigourous proofs in mathematical understanding. While undergrads and early grad students focus primarily on proofs, formalism recedes into the secondary role of honing intuition as mathematicians transition to the &quot;post-rigourous&quot; stage of their development[1].

          The importance of intuition in mathematics cannot be overstated. That&#x27;s why people go to math talks even when they have access to papers with formal theorems and proofs. In a less formal setting, they get to pick the author&#x27;s brain to understand their mental pictures and heuristics that don&#x27;t make their way into papers. Those would be analogous to chain-of-thought traces and agent-to-agent messages for a computer generated result.

          [1]: <a href="https:&#x2F;&#x2F;terrytao.wordpress.com&#x2F;career-advice&#x2F;theres-more-to-mathematics-than-rigour-and-proofs&#x2F;" rel="nofollow">https:&#x2F;&#x2F;terrytao.wordpress.com&#x2F;career-advice&#x2F;theres-more-to-...

      3. killerstorm · · focus · HN ↗
        The proof itself can be studied, either with AI or not.

        &quot;Intermediate reasoning traces&quot; might be interesting but they are not by any means requited.

        This letter has nothing to do with reasoning traces anyway: they just don&#x27;t want math research to be front-run by internal models, that&#x27;s all.

        1. gus_massa · · focus · HN ↗
          Also, in math most &quot;intermediate reasoning traces&quot; are erased and the solution only shows a simplified path that many times is only visible after the proof is complete.
    11. socializer · · focus · HN ↗
      &gt; akin to gatekeeping how someone should breathe air.

      Yes, and professions that do that - that vocally insist there is an essential human element to the craft - will likely fare better than the ones that say &quot;whatever, code is code&quot; or &quot;whatever, math is math&quot;.

      This is smart. We might not like it, but SWEs are actually the dumb ones with their utilitarian attitudes to AI. Meanwhile, professions such as writers or musicians are positioning themselves better by shunning &quot;artists&quot; that simply pull the lever of a gen AI system.

      1. fapjacks · · focus · HN ↗
        The difference, of course, is that people don&#x27;t care if their spreadsheet is written by an artisanal human programmer or just some stupid, swarthy Idea Guy banging on a keyboard. It seems that a lot of people do however care if the music they listen to or the art on their living room wall is made by a human or by a machine. Maybe it&#x27;s about &quot;positioning&quot; but I don&#x27;t think so. Most people want to pretend they are creatures of finer taste than everyone else around them. In this regard, I&#x27;m waiting for the other shoe to drop on AI in (for example) music, and there being kind of lip-syncing scandals with popular musicians.
      2. GPerson · · focus · HN ↗
        The other side of this is that there actually are utilitarian arguments for human involvement. Unfortunately SE is dominated by misanthropic types who dismiss these out of hand.
    12. isotypic · · focus · HN ↗
      To quote Noam Brown, &quot;Our main focus is shipping great models so everyone can use them to make discoveries of their own&quot; [1]. Spending 15 million dollars of compute with an internal model to blitz and scoop a resolution of Navier-Stokes that someone is already on track to resolve (or, from my understanding of why OpenAI did this, had already resolved, as staff at OpenAI stated their attempt was prompted by rumors of a resolution by Anthropic) is in complete opposition to this stated claim. That act is what this portion of the recommendation is in response to: OpenAI perpetually holding out internal models and tooling, using them to solve important problems in math, and thus themselves holding a monopoly on certain aspects of mathematics. Why is it absurd to ask people who are in a position to do an obviously damaging act to not do so, especially when those same people were the ones who asked for your advice in the first place and claimed to not want to do said act previously?

      [1] <a href="https:&#x2F;&#x2F;x.com&#x2F;polynoamial&#x2F;status&#x2F;2093451221273387477" rel="nofollow">https:&#x2F;&#x2F;x.com&#x2F;polynoamial&#x2F;status&#x2F;2093451221273387477

      1. ChickeNES · · focus · HN ↗
        Because it’s not a damaging act, to those who aren’t gatekeepers.
        1. isotypic · · focus · HN ↗
          How so? All it does it move who the &quot;gatekeepers&quot; are. OpenAI continuing to pump math problems into their internal models will only mean that if you want to be on the cutting edge of mathematics problem solving, you have to have access to internal OpenAI models. It takes what was previously an incredibly open field -- basically every paper is freely available on the arXiv, any given topic has probably 5 textbooks -- and turns it into one where the frontier is in the hands of a single company. If you are so against &quot;gatekeeping&quot; -- which I assure you, mathematicians are not doing, if you personally use an LLM to solve an important problem and write it up nicely (keyword: nicely) nobody will be mad at you -- why are you so happy to place the field into the hands of a singular entity?
          1. trhway · · focus · HN ↗
            &gt;if you want to be on the cutting edge of mathematics problem solving, you have to have access to internal OpenAI models.

            that is the way of technology. If i want to be just in the middle of the pack, not even a cutting edge, i have to buy a car, i can&#x27;t just walk everywhere in reasonable time. I have to use a phone, i go to the doctor for modern medicine, etc. - note that pretty much everything is private companies goods and private services.

            &gt;It takes what was previously an incredibly open field

            It was nice riding a horse among the open rolling hills.

          2. quantumspandex · · focus · HN ↗
            How about not trying to be always on the cutting edge ? Is mathematics a sport ?
            1. shank-false-rin · · focus · HN ↗
              Doing research is by definition to be on the cutting edge.

              AI labs don&#x27;t even need models to out compete mathematicians, they can employ enough mathematicians to out compete those who are not affiliated.

              The questions is whether if we want research to be held in a oligopoly.

        2. popalchemist · · focus · HN ↗
          It directly undermines human achievement - something some people have spent a lifetime in pursuit of - for the sake of marketing. OpenAI gains nothing at all; the mathemeticians on the verge of achieving a lifelong pursuit have their entire career trajectory and perhaps reason for being eviscerated without a thought. If the goal is to further mathematics, the mathemeticians are the ones who would best understand whether what OpenAI is doing is helping or hurting.
        3. GPerson · · focus · HN ↗
          The only reason the world has mathematics at all is because of mathematicians. Most of the value in these results is to the people who understand them, not to some random fantasy science fiction project you’re imagining is going to happen because navier stokes is solved.
      2. trhway · · focus · HN ↗
        &gt;was prompted by rumors of a resolution by Anthropic

        reminds an old sci-fi story where top engineers were shown a video of a genius inventor who invented anti-gravity and unfortunately died while testing his apparatus which was clearly anti-gravitating in the video. Thus believing that it is a solved problem, just need to rediscover the lost solution, the engineers quickly developed anti-gravity. The original video happened to be a fake specially created for that purpose.

        &gt;thus themselves holding a monopoly on certain aspects of mathematics

        Monopoly prevents others. In science me knowing something doesn&#x27;t prevent others from obtaining the same knowledge, especially in math where any knowledge is just a result of thinking.

        The math establishment is trying to bring into the math the rules and notions similar to those of the patent and trademark laws. Those attempts should be outright rejected.

      3. fasterik · · focus · HN ↗
        Frontier labs aren&#x27;t under any obligation to release every model they develop. Either way, I don&#x27;t see much evidence that they&#x27;re withholding them in perpetuity. Open models aren&#x27;t far behind so there&#x27;s not much of an incentive for that.

        Difficult math problems are useful benchmarks and milestones. It&#x27;s well worth throwing money at solving a problem if it drives competition and makes models 10% or 50% more intelligent. The benefits become available to everyone, including thousands of mathematicians who can use them to become more productive.

        1. parisbs · · focus · HN ↗
          &gt; Open models aren&#x27;t far behind so there&#x27;s no incentive for that. &quot;But inference costs play a massive role here too, which I think is still the biggest bottleneck in AI development. Running high-impact models for math, medicine, or programming requires a ton of compute. Throw in the politicization of everything AI-related, and it feels like model privatization is just the tip of the iceberg.&quot;
    13. fph · · focus · HN ↗
      [delayed]
      1. mathisfun123 · · focus · HN ↗
        jesus christ the number of asinine contrarian comments here is unbounded apparently

        &gt; you cannot practice without passing the bar exam

        you cannot represent other people in a court of law without passing the bar. you can absolutely read the law and represent yourself pro se.

        &gt; licensed individuals: medical doctors, journalists, electricians

        first of all you don&#x27;t need a license to practice journalism, the credentials are for the news agency itself. second of all doctors and electricians are licensed because there are material liabilities. you should read some more of that law that you&#x27;re gatekeeping...

        1. GPerson · · focus · HN ↗
          Have fun defending yourself in court with your AI companion. You’re living in a fantasy.
          1. mathisfun123 · · focus · HN ↗
            no one is talking about that? we&#x27;re talking about whether you need a license to use the law in your own defense?
      2. trhway · · focus · HN ↗
        &gt;The law is also a sequence of letters available to anyone. Yet you cannot practice without passing the bar exam.

        You still can be punished for violating a law even if you hadn&#x27;t passed the bar exam.

    14. AndrewKemendo · · focus · HN ↗
      I agree that this reads like they are clinging to the past for its own sake, rather than to have more predictable systems.

      I understand the instinct here, I just disagree with the idea that we should limit mechanical automation to the rate of human understanding. That’s a very low ceiling

    15. danielmarkbruce · · focus · HN ↗
      On top of that, many of the best mathematicians have stratospheric iqs. Do the mere mortals among us ask Terry Tao to stop using that big brain of his so the rest of us have a chance at proving some (mostly useless) math ideas?
    16. ComplexSystems · · focus · HN ↗
      It seems that, despite spending decades obsessing over their various niche problems, they have little interest in a magic button that can immediately produce the answer. At best they view this button as a mild nuisance they need to contain somehow.
      1. GPerson · · focus · HN ↗

        [dead]

    17. qnleigh · · focus · HN ↗
      If your life&#x27;s work were to get outsourced to AI and you lost your job&#x2F;the opportunity to do it, I doubt you would make this argument.

      I would rather live in a world where mathematicians get the opportunity to do math with AI, rather than AI companies doing the most important mathematical work and leaving them behind. I hope this for all professions that people want to do.

  3. unddoch · · focus · HN ↗
    For every important match problem solved by AI, without mathematicians we wouldn&#x27;t know about the existence and importance of the problem.

    Famous mathematical conjectures are social constructs, formed by decades of even centuries of attention given to them by members of the math community. Without it, the danger is that future math &quot;progress&quot; will be reduced to generating tables of Lean statements and a probable&#x2F;unprovable bit generated by AI.

    1. Xirdus · · focus · HN ↗
      Could just be a sampling bias. Humanity had something like 3000 years to make famous conjectures, whereas AI mathematicians have been around for a month or so. Give them time, I&#x27;m sure they&#x27;ll start formulating highly consequential unsolved problems soon enough.
      1. amoss · · focus · HN ↗
        Somewhat tiring that as alway any criticism is reduced to &quot;but have you tried this on the latest model&quot;.
        1. auggierose · · focus · HN ↗
          Maybe tiring, but that is the reality. Note that mathematicians are only upset now that &quot;have you tried this on the latest model&quot; works for so many of their problems now, but didn&#x27;t for the model before that.
        2. Xirdus · · focus · HN ↗
          Those are the two extremes, both are just as bad. Don&#x27;t excuse shortcomings of the current models with promises of future improvements. But also don&#x27;t demand literal miracles in 21 business days.
      2. eru · · focus · HN ↗
        Not just sampling bias, but also human bias.

        In a sense, how do you know whether the problem your AI has just solved is important? A simple proxy is to just check whether humans have thought it&#x27;s important.

        That&#x27;s also why famous open problems are a good benchmark or proxy: you don&#x27;t need to convince the rest of the world that the problem your lab&#x27;s new AI just solved is actually useful or hard.

        1. xanderlewis · · focus · HN ↗
          Not all of the &#x27;famous&#x27; open problems &#x27;mathematicians have failed to solve for decades&#x27; are actually that famous though. In some cases they&#x27;ve remained open because no one cared or had even heard of them. Those outside the mathematics community seem to think that all mathematicians can, and do, work on essentially all problems (for example, most mathematicians have in mind the millennium problems as a goal), but this is very far from the case. Most serious problem statements are not even particularly understandable to most mathematicians, let alone workable on.

          There&#x27;s also a difference between important and hard. There are important problems that turn out to be easy, and hard problems that turn out to be useless.

          As usual, I think everyone would agree that something like &quot;curing cancer&quot; would be both hard and important!

          I think the AI labs&#x27; current obsession with showing off mathematical results to uninformed outsiders is a cheap trick. If they were really interested in &#x27;enabling human flourishing&#x27; (rather than just wowing, by any means possible, investors with more money than sense), they&#x27;d be showing off cures to diseases rather than solving obscure problems in combinatorics only previously considered by three Russians fifty years ago and declaring that The Singularity is here.

      3. xanderlewis · · focus · HN ↗
        &gt; AI mathematicians have been around for a month or so.

        LLMs have been around for years, and they&#x27;re explicitly trained on the entire history of human mathematics (without which they&#x27;d be unable to do anything).

        1. Xirdus · · focus · HN ↗
          Yes, and they&#x27;ve done absolutely fuck all with this knowledge until very, very, very recently.
          1. xanderlewis · · focus · HN ↗
            That is what I&#x27;m saying. There&#x27;s a gold rush to extract what can be done with LLMs, but no indication that it&#x27;ll continue. Maybe it will, but the evidence for its continuation seems to be entirely hype based on the fact that. It&#x27;s not because &#x27;the capabilities are improving at a staggering rate omg the singularity is here guys&#x27;; it&#x27;s mostly because no one bothered to spend enough time and money (and currently absurd amounts are required) to give it a serious shot until recently.

            I like the test proposed by Demis Hassabis. Something like: train an LLM on pre-Einstein physics and see if it can rediscover what Einstein did. Despite the incessant noise online, we seem to be no closer to this. If there&#x27;s material evidence that we are, I&#x27;d sincerely like to hear about it!

            1. famouswaffles · · focus · HN ↗
              LLMs have improved at a staggering rate over the years. From spewing incoherent gibberish to barely managing low digit arithmetic to only tackling high school level problems.

              2 years ago, a DeepMind system achieved IMO Silver. This system was not a pure LLM, nor were the problems solved end to end in language. In fact the role of the LLM was to translate the problem into lean and generate strategies that could be auto verified. Some problems took up to 3 days to compute.

              One year ago, both OpenAI and DeepMind announced internal models had achieved IMO Gold. Unlike the cobbled together Alphaproof and AlphaGeometry, these results were purely LLMs, solved end to end in language, with any lean proofs generated by the LLM afterwards.

              Today, we have publicly available models capable of solving well known conjectures. And in less than the time it took Alphaproof&#x2F;Geometry to attain IMO Silver, internal models can even solve a millenium prize problem.

              Comments like yours just make it plain you aren&#x27;t paying any attention at all.

              1. xanderlewis · · focus · HN ↗
                &gt; internal models can even solve a millenium prize problem.

                OpenAI stole the work of Tristan Buckmaster to do it, and refused to explicitly deny it.

                What do you think has enabled the &#x27;staggering rate&#x27; of improvement? Scaling up? More data? It seems like, since LLMs do not solve problems from first principles and make crucial use of human work (without which they&#x27;d have nothing), once all the data has been eaten, some sort of plateau will indeed be reached. Anthropic are already reportedly buying up all of the world&#x27;s second-hand books and destructively (their words) scanning them in a desperate rush for ever more training data, so I don&#x27;t think this theory is unfounded.

                1. famouswaffles · · focus · HN ↗
                  &gt;OpenAI stole the work of Tristan Buckmaster to do it, and refused to explicitly deny it.

                  No they did not. Tristan (with heavy aid from LLMs) solved a sub-problem via a path Open AI&#x27;s full solution didn&#x27;t even use (forced vs unforced). To say they stole his work would be extremely silly.

                  And they explicitly say - “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.”

                  <a href="https:&#x2F;&#x2F;www.nytimes.com&#x2F;2026&#x2F;09&#x2F;10&#x2F;science&#x2F;tristan-buckmaster-openai-math-navier-stokes.html" rel="nofollow">https:&#x2F;&#x2F;www.nytimes.com&#x2F;2026&#x2F;09&#x2F;10&#x2F;science&#x2F;tristan-buckmaste...

                  &gt;What do you think has enabled the &#x27;staggering rate&#x27; of improvement?

                  Compute and data? So what?

                  &gt;It seems like, since LLMs do not solve problems from first principles and make crucial use of human work (without which they&#x27;d have nothing), once all the data has been eaten, some sort of plateau will indeed be reached.

                  Data used to train the models has become increasingly synthetic. The reinforcement learning getting these models superhuman at math isn&#x27;t tied to human data.

                  &gt;Anthropic are already reportedly buying up all of the world&#x27;s second-hand books

                  That is not what they are doing.

                  &gt;What do you think of the Hassabis Test? Until it passes, I don&#x27;t see how humans are replaced.

                  I don&#x27;t much care about it. Neat idea but a waste of time. There&#x27;s not enough pre-einstein text digitzed to make a fair shot at it. And it&#x27;s kind of meaningless. You&#x27;re already in the midst of AI becoming superhuman in one domain. If you want to stick your hand in the sand about it then that&#x27;s on you.

                  1. xanderlewis · · focus · HN ↗
                    &gt; To say they stole his work would be silly.

                    He says they stole it; see for example his recent interview with Numberphile. So is he silly? Or do you know better?

                    &gt; There&#x27;s not enough pre-einstein text digitzed to make a fair shot at such an experiment

                    Then why was it possible for humans to do physics, or indeed function at all, pre Einstein? I guess humans are special after all.

                    1. hardbass · · focus · HN ↗
                      He has the right to present his side. Without analyzing both sides claims, no comment can be made.
                      1. xanderlewis · · focus · HN ↗
                        There is an important asymmetry, though: Buckmaster is a mathematician in it for fun (as almost all mathematicians are, because there certainly isn’t much money in it), and OpenAI is a company desperately scrambling for anything they can present as evidence that the singularity is here and you must invest your money now. Buckmaster abides by the unwritten code of mathematicians (alluded to in said interview); OpenAI abides by absolutely no such code other than ‘move fast and break things’.

                        I don’t think it’s a stretch to say that each side’s claim is equally trustworthy.

                        1. hardbass · · focus · HN ↗
                          But there is strong ego involved on part of Mr Buckmaster, egos tend to cloud judgement and bias a person. I would not speculate on either side and I would be careful to avoid people who simply take one side for granted.
                          1. xanderlewis · · focus · HN ↗
                            Listening to him, I didn’t get that impression. I get that academia at large is full of egomaniacs (or so I’ve heard and read online), but the mathematics community is a weirdly non-toxic oasis of reasonable enthusiasts — genuinely, surprising though that may be to those with no experience!

                            So I have my reasons to weigh his statements more heavily. I certainly don’t take anything for granted.

                            1. hardbass · · focus · HN ↗
                              I don&#x27;t mean he must specifically be an egotistic person. But if you feel slighted and a problem you have been working hard for months taken from under you, any person would have a egotistic bias.
                    2. famouswaffles · · focus · HN ↗
                      &gt;He says they stole it; see for example his recent interview with Numberphile. So is he silly? Or do you know better?

                      He can say whatever he wants. I&#x27;m not obligated to take it at face value, especially when it seems to fall apart with some scrutiny.

                      &gt;Then why was it possible for humans to do physics, or indeed function at all, pre Einstein? I guess humans are special after all.

                      Billions of years of evolution probably has something to do with it.

    2. jillesvangurp · · focus · HN ↗
      You make a good point about LLMs being (so far) great at identifying solutions to complex puzzles but not yet coming up with their own theories, questions, etc. The business of finding interesting questions to answer rather than answering them is the essence of what scientists do. Good science identifies more questions than it answers.

      With Fermat&#x27;s theorem, the genius was in the original theorem. Which then caused generations of mathematicians to break their heads over trying to prove it correct. Fermat didn&#x27;t write down a proof. His theorem was famously just a scribble in a side line of a book. Probably it was something that he had an hunch about that he couldn&#x27;t quickly falsify.

      I don&#x27;t think AI is being used much for coming up with new problems yet. But I don&#x27;t see why that would not be possible either. It&#x27;s the obvious next frontier after AI clears the backlog of existing theorems. I imagine scientists are already using AI to find new interesting problems to work on and generally explore the problem space. But fundamentally, the reflex of asking or imagining &quot;if this is true, what else could be true&quot; is something that distinguishes people from AIs. For now at least.

  4. Animats · · focus · HN ↗
    This paper wants AI companies to pay human mathematicians to understand AI-generated stuff. That&#x27;s an unusual ask.
    1. NewsaHackO · · focus · HN ↗
      I would describe it as close to rent seeking
    2. Joel_Mckay · · focus · HN ↗
      Many wrongly assume actual problem solving can be automated with an LLM with more data. Rather... LLM are good at finding similar context in isomorphic plagiarized works, with little actual &quot;AI&quot; in anthropomorphized marketing. Likely also effective at targeting individuals and organizations as hapless intelligence targets. =3

      <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Nbwv5wHQoj0" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=Nbwv5wHQoj0

    3. unddoch · · focus · HN ↗
      If youre going to spend 10 million dollars on 10000 agents trying to solve some important maths problem I think it&#x27;s reasonable to ask for some grants to help digest whatever they came up with. Or you could hire mathematicians and do it in-house, but I guarantee you grants to PhD students are cheaper than silicon value salaries.
      1. ChickeNES · · focus · HN ↗
        Why pay for grants when you can just spend the money on compute more efficiently?
        1. eli_gottlieb · · focus · HN ↗
          Because the compute isn&#x27;t gonna turn AI slop into a clear, readable paper.
          1. gus_massa · · focus · HN ↗
            Not for now, but it&#x27;s AI is getting better. A big step is &quot;refactoring&quot; a very long proof into a few intermediate lemas and theorems that are more inteligible and useful for other proof. It may take a few years or decades in some cases.

            Anyway, I expect AI to be better at &quot;refactoring&quot;, but for now a centaur is better.

            1. hodgehog11 · · focus · HN ↗
              Actually, for what you are mentioning, it is getting worse. There was a sweet spot somewhere around the release of GPT-o3, and ever since, the LLMs have been getting more accurate at solving problems, but worse at explaining how, and to hone in on what is interesting. This isn&#x27;t surprising, as RL strategies shifted from RLHF to RLVR, so priorities during learning changed. I don&#x27;t expect AI labs to reverse course on this. We can expect AI proofs to become increasingly incomprehensible over time.
              1. gus_massa · · focus · HN ↗
                I still remember Garry Kasparov vs. Deep Blue. Now, Magnus vs Stockfish is not even funny. I&#x27;ve seen AlphaGo and AlphaStar, and how their communities reacted...

                I remember when Mathematica only could tell the answers and you had to type the formula correctly. Now there are apps that solve the exercise from a photograph with all the intermediate steps. We reminded the T.A. to be more alert during the midterms becuse we already had problems. I&#x27;m very worry about the magical glasses now, but it&#x27;s important to be not overreact and be polite with the students.

                Back to refactoring unintelligible long math proof: Let&#x27;s talk again in 2031.

          2. GPerson · · focus · HN ↗
            The paper is secondary to developing a general understanding of new ideas. The AI is not going to do that. All of the AI bros in this thread are going to be addicted to super AI Netflix and the math community will be dead.
            1. eli_gottlieb · · focus · HN ↗
              The paper, both writing it and reading it, are a means by which we develop our understanding of new ideas. We can surely come up with a better means if we try, but &quot;stop trying and leave actual understanding to machines&quot; ain&#x27;t gonna cut it.
              1. GPerson · · focus · HN ↗
                Right we agree.
      2. 6510 · · focus · HN ↗
        They aren&#x27;t buying tokens, more likely it costs them 1m to run the 10000 agents for 88 hours. Still leaves room for the PhD ofc.

        I&#x27;m trying to map it on other fields and cant help but think it is absurd. If some company spends 1m developing a new alloy, should metallurgists be upset when they publish the recipe?

        1. GPerson · · focus · HN ↗
          It was a lot more expensive than this… Just look up the estimates before making stuff up.
    4. fultonn · · focus · HN ↗
      AI companies are already paying human mathematicians, to help train their models. Including to understand AI-generated stuff. The pay is kind of shit but still quite a lot better than what we were paid as phd students, especially if you do it 40 hours a week (which, tbf, was very short week in grad school).

      I know this because I spent a lot of social time around a Math dept in grad school and many of them are moonlighting working for subcontractors on production and evaluation of training data.

      Anyways, mathematics is a bit of a funny discipline... some buckets:

      There are lots of obvious cases where progress has obvious applications for incremental progress, and where you can ask for novel math from the perspective of the application or ask for applications from the perspective of novel math. That seems like the sort of thing that you could throw $10M at get something valuable without much human input. I do this, at much much much smaller dollar amounts, pretty regularly, and with open models, so nothing secret&#x2F;sota&#x2F;etc.

      But there are also lots of cases where some progress gets made on something very pure and esoteric and the implications aren&#x27;t really clear. Those are cases where just asking a bunch of nerds to marinate on it while interacting with a messy world in the full social generality of a modern university could make a lot of sense. The connection between the four color theorem and register allocation, for example, feels very... hard to do without humans free-associating in a diverse academic environment.

      And, at last, there are cases where there are subfields or problems that are big and important in the way that driving a rare car or wearing a particularly fascinating rolex is important. Some of modern mathematics feels like it has its cultural roots in intellectual gamesmanship amongst wealthy gentleman and&#x2F;or those under their patronage. That culture persists. A lot of the... less well-argued... objections come from this set.

      Like I said, math is kind of a uniquely weird discipline. It&#x27;s got aspects of practical gritty science, noblesse oblige&#x2F;high-culture, fashion&#x2F;taste, craftsmanship, tutelage, and so on.

  5. kingstnap · · focus · HN ↗
    Mostly pretty straight forward. The idea that proofs be desloppified, attribute existing literature properly, and published somewhere expediently where it can be commented on, with artifacts for verification, is all very uncontroversial stuff.

    I think the spicy take is definitely this stance that longstanding mathematical problems shouldn&#x27;t be used as benchmarks for (specifically proprietary) models. Stated right at the very top.

    The justification is pretty clear.

    &gt; The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline.

    It is all fun and games (for non mathematicians) when mathematicians can&#x27;t compete with AI labs but I think the more dangerous direction is when this starts being true for the rest of everything. For example cybersecurity or whatnot. Hence why I think Anthropics whole stance of being completely against open anything is actually *extremely* dangerous due to the centralization of power which they completely ignore as a risk factor.

    The most discussable thing in this is certainly the idea that labs should fund mathematicians to do expositions.

    &gt; One of our principles is that AI labs have a responsibility to provide support, including funding, for the development of human understanding of the AI mathematical output that they release.

    Obviously this directionally sounds like the role of mathematicians would be shifting towards interpreting AI results instead of making proofs. I&#x27;m not sure who would should really be billed for that. Plus how would you decide who gets the grant?

    An interesting thing is that by stating that that the lab that dropped the result provide the funding, this is *directly* proposing an example of taxing AI labs for displacing knowledge workers.

    1. BobbyJo · · focus · HN ↗
      &gt; The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field

      This is literally the economic bet of the big labs in the broader economy. You use your relative advantage to front run or outcompete.

      I&#x27;m not sure this argument will work given it is essentially an argument against the thesis the big labs use to justify their valuations.

      1. tehjoker · · focus · HN ↗
        Right, the whole idea of these labs is to install themselves as capitalist philosopher kings. They won&#x27;t tolerate any ideas of &quot;decentralization&quot; despite it benefiting 99% of humans.

        OpenAI was started because Elon and Sam thought Demis was going to make himself dictator and they wanted a piece of that action (reading between the lines). All the labs, even Anthropic have the same idea dressed in different marketing gloss. The major exception (I imagine) are Chinese labs, since the Communist Party of China will demand control over these labs and their models. Good! Democratic human control is a good thing. Certainly, there is more democracy in China than in America. That&#x27;s the idea of socialism, democracy for the workers, not for the capitalists (we do the inverse).

        1. octoberfranklin · · focus · HN ↗
          When you used the words &quot;decentralization&quot; and &quot;socialism&quot; in the same post I kinda puked a little bit.
          1. tehjoker · · focus · HN ↗
            Socialism is about the decentralization of power. In some popular formulations, the economy is run according to a central plan, but in one view, this is democracy. Otherwise, you are at the whim of the rich and tyrannical market forces. With central planning, you get a vote on the general direction of society, which has its possibilities encoded in the material world.
            1. octoberfranklin · · focus · HN ↗
              Socialism is a form of government, which is the ultimate centralization.
              1. thunderfork · · focus · HN ↗
                Centralization of what, though? It could centralize operations while (through, eg, democracy) decentralizing power
        2. graemep · · focus · HN ↗
          You end with some pretty far fetched claims there. Control by an authoritarian government is no democracy. I am sure that the people running AI companies will claim they intend to do it for the good of society, just as the Chinese government already does.
      2. genxy · · focus · HN ↗
        Once they get good enough, they won&#x27;t even ship the models, they will just replace all the jobs themselves. This is where Anthropic, OpenAI and Google are heading, esp Google with GSuite, it already is up in your business doing your business.

        All your jobs are belong to them.

    2. meowface · · focus · HN ↗
      Am I the odd one, or is this, like... absolutely insane logic?

      &quot;The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline.&quot;

      Are mathematicians&#x27; private brains unfair if they&#x27;re way better at solving open math problems than anyone else? Are they required to share everything they&#x27;re working on, as they&#x27;re working on it?

      Should Andrew Wiles have been condemned? Wouldn&#x27;t these arguments all have applied to him? Besides him working at more human speeds.

      1. octoberfranklin · · focus · HN ↗
        Capital can&#x27;t buy you a better brain. It can buy you GPUs.

        The question is whether we want mathematics to be dominated by whoever has the most capital. This is perilous because mathematics doesn&#x27;t produce profits like commerce does. The AI labs might end up killing something off that they are unable to sustain a replacement for.

        1. thfuran · · focus · HN ↗
          What exactly would they be killing off and how?
        2. hardbass · · focus · HN ↗
          I would argue that mathematicians need an even more level playing field. Many mathematicians including Alpoge were using AI&#x27;s, other mathematicians used heavy computing power for their work eg the four color theorem. So we should set strict token&#x2F;flop&#x2F;dollar limits for mathematicians. IQ is also an unfair advantage, so an IQ limit should also be enforced for mathematicians.
      2. emil-lp · · focus · HN ↗
        It&#x27;s not insane when you realize that in mathematics, the goal isn&#x27;t theorems (we have always been able to generate correct theorems, this is a basic programming exercise).

        The goal is to expand and extend our understanding.

        When an LLM produces a proof, nobody (including the LLM) gained new understanding ... Unless, of course, a human being sits down and understands it, and communicates the new understanding to the broader community.

        1. Calazon · · focus · HN ↗
          The insane part is placing the burden on AI labs to advance mathematical understanding. Why should this be their responsibility?

          If they want to simply generate theorems and proofs and post them on the internet, why not? Does doing that really inflict &quot;substantial negative externalities ... on the mathematical community&quot;?

          1. meowface · · focus · HN ↗
            [delayed]
          2. curt15 · · focus · HN ↗
            If math is a &quot;burden&quot; on AI labs, why do they spend tens of millions of dollars to race a researcher to a theoretical result? What&#x27;s the ROI for that when OpenAI is already notoriously cash-strapped? Their motives cannot be ignored here and implicitly pervade the entire discussion.
            1. meowface · · focus · HN ↗
              ...Could you not ask this of anyone who works on pure math problems? What on Earth are you talking about??

              &quot;Academics are paid paltry salaries, university departments are cash-strapped, why are they studying these abstruse math problems instead of building rockets?&quot;

              Successfully advancing fields of math and science is a good thing. Why would they not do it. Why would they not want to prove their increasingly intelligent computers are able to solve unsolved, complex math problems humans have failed to solve for centuries and then release the solutions to the public. What do you want them to do, not try to solve them?

              1. pegasus · · focus · HN ↗
                They are not advancing the field. At least they didn&#x27;t in the case of the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.
            2. Calazon · · focus · HN ↗
              Presumably some combination of marketing existing models and training&#x2F;improving future models.

              My point was about what is and isn&#x27;t the responsibility of AI labs. Why should they be required to invest more (or fewer) resources into math than they otherwise want to?

              (If you ask me, safety and security are what they need to invest more into.)

              1. pegasus · · focus · HN ↗
                Simple. Because they are benefiting from output of the math community, in fact they were required for creating these models in the first place.
        2. steinwinde · · focus · HN ↗
          Is it not more democratic, if AI companies announce new theorems and proofs, and the discipline of mathematics furthers &quot;our understanding&quot; - instead of that the wealthiest universities in existence (all of them in the US) use their advantageous access to AI to produce them, along with their exclusive furthering of our understanding?

          In a world, where expensive AI models running thousands of agents produce the most remarkable results, how should the discipline of mathematics look like, when money and access to compute plays such a pivotal role?

          With the Navier-Stokes solutions being out in the wild, any mathematician at an impoverished university can make a stab at it and help our understanding. Would the solutions being held back by those who produced them at Havard &amp; Co. (until they have their nice articles ready), what is the role of mathematicians in less affluent universities?

          I do not assume AI companies will be ready to provide equal access to their AIs to worldwide mathematics.

        3. rafaelero · · focus · HN ↗
          Isn&#x27;t easier to understand something backawards? It seems much simpler to understand something once you already have the solution.
        4. [deleted] · · focus · HN ↗

          [deleted]

      3. qnleigh · · focus · HN ↗
        I see two separate arguments in favor of this logic:

        1. Academic mathematics has traditionally been meritocratic, and this is a good thing. If you work hard and demonstrate results, then you will be given further opportunities to do math research and the resources to do it. We are concerned that AI will reward money and access to frontier models instead.

        2. There is a general concern that AI could lead to massive accumulations of wealth (see concerns of massive job displacement). AI companies claim that they want to raise standards of living and benefit humanity, which means that they will need to share their resources and wealth in some way. If they effectively destroy the mathematical community be racing ahead and taking all the major results for themselves, that does not bode well for the rest of us. It seems like a great opportunity to show the world how AI will benefit humanity rather than replace it.

    3. zozbot234 · · focus · HN ↗
      &gt; Mostly pretty straight forward. The idea that proofs be desloppified, attribute existing literature properly, and published somewhere expediently where it can be commented on, with artifacts for verification, is all very uncontroversial stuff.

      If Ramanujan could freely disclose and publish results that were arrived at by literal divine inspiration (he certainly didn&#x27;t bother to write down &quot;proofs&quot; in the modern sense!) why do we suddenly need all this &quot;responsible release&quot; process stuff when it comes to AI-derived results? This makes no sense when compared with existing norms within the mathematical community.

      1. hodgehog11 · · focus · HN ↗
        He could not freely disclose and publish his results, that was the whole problem. He only got traction when one result was automatically validated because Hardy had already seen it. His findings more broadly were only considered fine once they were understood and verified. This declaration is basically the same thing. Having Lean code doesn&#x27;t substantially change that.

        It&#x27;s almost like a lot of non-mathematicians are commenting and have no idea about how the field really works. Or at least, how it works at the top level.

      2. GPerson · · focus · HN ↗
        Trillion dollar corporation != 1 guy who read a big textbook.
    4. killerstorm · · focus · HN ↗
      Mathematicians can only make these demands because they believe that AI labs get a lot of credibility from math results. So they propose a trade: we give you credibility, you give us funding and let us to gate-keep.
      1. GPerson · · focus · HN ↗
        The “gate keeping” you’re referring to is purely imaginary. I have no idea why people believe this.
    5. aaron695 · · focus · HN ↗

      [dead]

    6. thfuran · · focus · HN ↗
      &gt;Anthropics whole stance of being completely against open anything is actually extremely dangerous due to the centralization of power which they completely ignore as a risk factor

      I really don’t see it as an oversight. It’s the goal.

      1. hodgehog11 · · focus · HN ↗
        Nah, it&#x27;s the whole benevolent dictator mentality that these socially maladjusted individuals believe. If you believe that you are the only good guys, you are likely the bad guys.
  6. areoform · · focus · HN ↗
    I applied to the caltech mathaton.

    While applying, I looked at the current SoTA, (briefly) read through some of the papers, and realized that I am very far away from understanding them.

    Understanding one of these proofs is the work of several months, years or lifetimes depending on whether or not something clicks. It requires a kind of stamina that I quite frankly don&#x27;t have, but I would like to develop.

    If the mathaton&#x27;s organizers accept my team, I realized that I would spend the next few years working through the result.

    So why apply to the Mathaton?

    &quot;Many years ago the great British explorer George Mallory, who was to die on Mount Everest, was asked why did he want to climb it. He said, &#x27;Because it is there.&#x27;

    Well, [theoretical math] is there, and we&#x27;re going to climb it, and [topology] and [number theory] are there, and new hopes for knowledge and peace are there. And, therefore, as we set sail we ask God&#x27;s blessing on the [~~most hazardous and dangerous and greatest adventure~~] on which [we have] ever embarked.&quot;

    More seriously, I applied because I was hoping to get access to the models without the veil. I don&#x27;t think people realize just how big the gap is between what exists behind the scenes at these entities, and what we get out here.

    And it&#x27;s frustrating. Because I think it&#x27;s within the rights of frontier labs to decide whether or not to sell access to a product, but the labs aren&#x27;t just doing that. They&#x27;re trying to thumb the scale to make sure that none of us ever get access to these models at peak performance. Ever.

    And I think humanity is worse off for that. I am worse off for that.

    I have studied the shape and structure of historical technological revolutions (and I&#x27;ve written about it), and usually the world doesn&#x27;t realize how big of a big deal the big deal is because the big deal is often flawed, broken, and under-delivers. In the short term.

    In the long term...? The world changed in the past few months. I think mathematics is one small part of that.

    For most of human history, higher mathematics would have been inaccessible to me, and other outsiders, no matter how well heeled. Mathematics is, or rather was, a living discipline that existed piecemeal in a handful of minds across the world. These people&#x27;s time was finite and valuable. To just meet them, you&#x27;d have to jump through hoops, and spend years proving yourself.

    There is no price for an hour of tutoring from Terance Tao. But now, with AI? You can have an entity with the capabilities of Terry Tao help you understand the subtleties of math.

    AI has changed what mathematics is. And every prominent mathematician seems to know it. They feel like mathematics has been devalued, and in some ways it has. Mathematics has gone from being a living discipline kept alive by a chosen few to a wellspring everyone can sip from. For the first time in human existence, learning and accessing higher mathematics doesn&#x27;t involve jumping through hoops and knowing the right people. You can just ask.

    I can just ask.

    Except I can&#x27;t. Because that capability is being gate kept. And I want to know. I want to climb the mountain.

    1. wbl · · focus · HN ↗
      &quot;There is no royal road to Geometry&quot; - Euclid. Mathematical knowledge isn&#x27;t from tutoring but doing. And no one is against the AI helping explain the tricky parts to help you practice. Rather it&#x27;s about dumping a giant bunch of low quality text with some Lean claiming a big result is done.
      1. areoform · · focus · HN ↗
        Yes, it&#x27;s why I love math. You can&#x27;t buy fluency.

        There are subtleties to mathematics that aren&#x27;t easy to understand from the written page alone. It&#x27;s why it&#x27;s a living medium.

        For example, as we&#x27;re talking about LLMs... why not, there are ways to reason about vector spaces that weren&#x27;t intuitive for me to understand. It&#x27;s something that required talking things out with a friend who is a practising mathematician (albeit in training).

        I am not smart enough to reconstruct all of mathematics on my own from scratches on paper alone. That back and forth is necessary. And it&#x27;s something that you couldn&#x27;t have &quot;bought&quot; for cutting edge math at any price a few months before this point in time. Because it exists in the minds of people and it needs lots of back and forths with those people.

        It&#x27;s why LLM proofs can be slop on paper. A proof that no one can check or understand is not but scratches on paper. BUT LLMs are also the solution to the problem they create. The machines that can generate proofs are also machines that can help us understand them.

        The living medium can now be represented and scaled inside of a machine. I can now sit down at an airport and have that discussion. I think that&#x27;s transformative for our species.

        1. echelon · · focus · HN ↗
          &gt; You can&#x27;t buy fluency.

          Just wait until BCI and&#x2F;or fast Pavlovian conditioning force fed by agents into human learners.

          I&#x27;ve been vibe coding my own SRS software that is vastly superior to my learning style than Anki, and I know I&#x27;m just scratching the surface of accelerated learning. Who knows where this goes.

          MRI and glucose injections with agent-tutor steering and millisecond feedback to learning?

          We might be able to Matrix &quot;I Know Kung-Fu&quot; things into brains one day.

          1. fragmede · · focus · HN ↗
            You might need to add in chemically altered states of consciousness and magnetic stimulation of the right areas, but yes.
    2. omnicognate · · focus · HN ↗
      &gt; Except I can&#x27;t. Because that capability is being gate kept.

      In what way are these &quot;gatekeepers&quot; stopping you asking an LLM questions about maths?

      1. areoform · · focus · HN ↗
        I would like to ask you a question.

        Can you, I, or any mathematician who isn&#x27;t well connected (let&#x27;s say someone who is a young Maryam Mirzakhani or just someone who is in grad school) learn from the system that produced the solution to the unit distance problem? <a href="https:&#x2F;&#x2F;cdn.openai.com&#x2F;pdf&#x2F;74c24085-19b0-4534-9c90-465b8e29ad73&#x2F;unit-distance-remarks.pdf" rel="nofollow">https:&#x2F;&#x2F;cdn.openai.com&#x2F;pdf&#x2F;74c24085-19b0-4534-9c90-465b8e29a...

        You will notice that it says on the first page,

            &quot;first mathematically generated in one shot by an internal model at OpenAI&quot;
        Mathematicians want to talk to the exact model variant whose summarized chain of thought is, <a href="https:&#x2F;&#x2F;cdn.openai.com&#x2F;pdf&#x2F;1625eff6-5ac1-40d8-b1db-5d5cf925de8b&#x2F;unit-distance-cot.pdf" rel="nofollow">https:&#x2F;&#x2F;cdn.openai.com&#x2F;pdf&#x2F;1625eff6-5ac1-40d8-b1db-5d5cf925d...

        And I want to talk to models of similar aptitude and capability to help me understand nuances of the proof. Mathematicians will happy to pay for this. I&#x27;ve heard that people and non-profits are putting together $$$ for this to get access to these systems so that they can all interrogate them.

        But the issue is that we can&#x27;t. And I&#x27;m using the royal we here.

        The paper says that the labs shouldn&#x27;t release proofs from models that mathematicians can&#x27;t interrogate. It&#x27;s very clear that the models we get as users aren&#x27;t the models used to produce the breakthroughs. And as LLMs display emergent capabilities, it&#x27;s uncertain whether or not the model actually understands what it&#x27;s explaining.

        Because if I don&#x27;t understand it. Professional mathematicians who are subject experts don&#x27;t understand it. Then how do we know the model does? How do we know that it&#x27;s correctly representing the proof produced by a more capable model? It&#x27;s not logical to take any random model at its word, unless we can verify. Or, if it&#x27;s the same model that produced the proof.

        And that&#x27;s what the mathematicians want. Access to the actual models.

  7. aidiscoverywire · · focus · HN ↗

    [dead]

  8. Der_Einzige · · focus · HN ↗

    [dead]

    1. ted_dunning · · focus · HN ↗
      In normal English usage, &quot;with extreme prejudice&quot; is commonly understood to mean that you advocate killing the person in question.

      Either you don&#x27;t know what you are saying and should improve your language skills

      Or you do and should be dropped from this site for advocating violence.

  9. mchusma · · focus · HN ↗
    Either mathematical progress helps advance society, in which case progress is a good thing.

    Or mathematics is more like a hobby, and while ai may spoil their fun, they need to move on like chess and go players.

    1. simianwords · · focus · HN ↗
      I agree. Its so strange to see an institution externalising their specific problems. If they have a problem, they should adapt and fix it amongst themselves.
      1. GPerson · · focus · HN ↗
        It’s so strange to see bootlickers like you at every turn cheering on the death of humanity. You’re one of the worst people on this website.
    2. winwang · · focus · HN ↗
      Or mathematicial progress helps advance society and AI mathematical velocity doesn&#x27;t offset certain blows to human mathematical velocity yet, so we get to lose progress for the good of an AI company&#x27;s advertisement.
      1. auggierose · · focus · HN ↗
        We don&#x27;t lose progress by AI solving Navier Stokes. Get a grip on yourselves.
        1. GPerson · · focus · HN ↗
          You have no clue what you’re talking about yet you’re making some big claims. Amazing.
          1. auggierose · · focus · HN ↗

            [dead]

    3. xanderlewis · · focus · HN ↗
      That’s a false dichotomy.

      Mathematical progress does (quite obviously, on the whole) help advance humanity, so progress is a good thing. The problem is that defunding mathematicians and handing over control to AI and the companies that create them will cause the subject to stagnate. Sure, for a while we might get progress on existing questions using (perhaps quite novel) combinations of existing techniques, but, so far, given the character of the results we’ve seen, there’s no indication that it will continue indefinitely. Even if it did, what would be the point? Huge textbooks full of work no one can understand or benefit from?

      One possible analogy is that humans work to add new points to the space of mathematical knowledge, and AI then fleshes this out to attain the ‘convex hull’ of these points. Essentially, humans ‘invent’ the definitions and pose the questions and AI does the grunt work as well as some creative exploitation of known results and tools to bring down all the low-hanging fruit that follows (important note: what appears to be non-low-hanging fruit to us may in fact be technically low hanging once AI is involved; we saw this for example with the Jacobian conjecture). This seems to be the current situation, and to argue that humans are fully replaced it is necessary to argue that AI is adding points outside the convex hull of human mathematics. A sufficient example would be a first-principles AI proof using alien techniques, and this we haven’t seen so far.

      The mathematics-chess comparison is, to put it bluntly, nonsense. I see where it comes from, but, as absolutely anyone with any research experience will tell you, mathematics is orders of magnitude (and this really isn’t strong enough) more open-ended, and doesn’t consist of a game one is seeking to ‘win’. The goal is understanding itself.

      1. DoctorOetker · · focus · HN ↗
        I think we need to start looking at another approach, can we create interactive reflex games that upload the knowledge from LLM&#x27;s or perhaps domain specific ones for formal mathematics, so that mathematicians get a similar level of access to the domain of discourse as the LLM?
    4. mrheosuper · · focus · HN ↗
      Whatabout mathematical progress that ruins humanity even more ? e.g a much more addicted algorithm than tiktok&#x2F;facebook reel.
      1. avazhi · · focus · HN ↗
        What about it? That’s not a mathematical issue.

        That’s like saying ‘what about the guy who walks to his ex wife and shoots her in the head’ as an attempted criticism of walking.

  10. simianwords · · focus · HN ↗
    I disagree with this.

    OpenAI should be allowed to produce whatever it wants but it just can&#x27;t claim that it has actually solved without the due process like peer review. If for example OpenAI solves a new conjecture, OpenAI should be free to publish it in their blog or arxiv in whatever way they desire. It can be slop, it can be non-slop. No one should police it.

    Mathematicians are free to use it or discard it. They shouldn&#x27;t externalise their concerns and restrict labs.

    Mathematics is seen today as the noblest and most aristocratic of professions. Turns out, AI disrupts it because access to capital&#x2F;compute now decides the results. Mathematicians don&#x27;t like this corruption - understandable.

    Its like guild of accountants opposing the calculator and require a responsible release. haha

    1. tttr · · focus · HN ↗
      There’s a reason why many of your posts are downvoted.
    2. freecodeio · · focus · HN ↗

      [dead]

  11. LelouBil · · focus · HN ↗
    [delayed]
    1. fasterik · · focus · HN ↗
      I&#x27;m not a mathematician either, but I find it hard to believe we could run out of problems in pure mathematics. Pure math is like a game where if you get bored you can invent new rules. Maybe eventually all fields related to applied problems will be settled, and the value of pure mathematics will be relegated to the status of other games like chess and go. But that&#x27;s so far away from current reality that I can&#x27;t imagine it happening in the next century at least.
      1. GPerson · · focus · HN ↗
        If you’re not a mathematician why are you chiming in to contradict one of the best mathematicians in the world? I don’t understand the lack of humility on this website.
        1. fasterik · · focus · HN ↗
          Because that&#x27;s an appeal to authority, which is a fallacy. Things aren&#x27;t true because one expert says they are, they&#x27;re true because there are arguments and evidence for them. I gave my reasons for thinking that the statement is wrong. It&#x27;s not a lack of humility, it&#x27;s just stating an opinion and giving reasons for it. If there were data showing that 90% of research mathematicians think we&#x27;re at risk of running out of problems, then I&#x27;d update my beliefs accordingly.
          1. xanderlewis · · focus · HN ↗
            No one’s saying you have to believe whatever the famous mathematician says — that would be stupid. They’re saying that there’s a difference between the opinion of an expert and some random outsider.

            This is true of all subjects, but it’s hard to think of a subject where the gap is as stark as it is in mathematics — even intelligent outsiders have no idea what the subject is really about, and, even worse, they think they know (mainly because we all studied something also called ‘mathematics’ as children and assume that research mathematicians probably do something similar).

            Feel free to speak, but understand that it doesn’t carry much weight.

            1. fasterik · · focus · HN ↗
              I dunno, it&#x27;s a weird take on a website dedicated to casual discussion of technical subjects to say that I shouldn&#x27;t chime in because I&#x27;m not an expert. I stated an opinion, and I don&#x27;t see anywhere that I presented myself as some sort of authority. Also, it&#x27;s beside the point, but for what it&#x27;s worth I have taken upper level undergraduate courses in pure mathematics (real analysis and two semesters of combinatorics), so I have at least some idea of what research-level mathematics looks like.
              1. xanderlewis · · focus · HN ↗
                I agree, though it might not be what you mean!

                I get pissed off reading the ‘weird takes’ on mathematics from people who come from the tech world and don’t know what they’re talking about (but for some reason think they do). Not only is it just painful to read; it’s actively harmful.

                Mathematicians are largely ignorant of software and are aware of and will freely admit to their own ignorance, but for some reason the software engineers here are largely ignorant or mathematics AND think they know it inside out.

                It sounds like you’re actually more well informed than most. Don’t take my comments personally, in any case.

              2. GPerson · · focus · HN ↗
                I’m sorry you feel like such a victim but it’s a topic in which having an awareness of how the mathematics culture works matters, which honestly should go without saying. You’re pitting yourself, someone with no understanding of the system, in direct contrast to someone who understands the system very well. You have no evidence for your view either. You’re just contributing noise.
                1. fasterik · · focus · HN ↗
                  I don&#x27;t think I&#x27;m the one adding noise here. You&#x27;ve done nothing but put words in my mouth and attack me personally without adding anything substantive to the discussion.
                  1. GPerson · · focus · HN ↗
                    You’re free to generate an arbitrary set of axioms and study the consequences. Zero people will care. People care about doing mathematics in a community, working toward recognizable goals.

                    The infinitude of mathematics doesn’t matter. What matters if mathematics doesn’t change radically is the size of the database of AI results relative to the potential output of a human lifetime.

                    You don’t actually understand what argument from authority is. There’s an actual reason the “authority” here is being appealed to which is not just their authority. You don’t respect people who know more than you, but you should still read Terence Tao’s mathstodon posts on stripmining mathematics.

    2. mikestylz · · focus · HN ↗
      In the past we might have said horses, stone, and bronze were three things necessary to advance civilization. In the future I&#x27;m sure the AIs will prompt themselves with nice problems. But for now I agree with AGMAI that we should be careful not to disrupt the field too severely. It&#x27;s reasonable to keep it around even if it&#x27;s just functioning as a temporary &quot;strategic reserve of expertise&quot;
    3. avazhi · · focus · HN ↗
      If you need people to invent problems to solve, you may not be working in a useful area.

      Time to get training as a plumber or electrician, I’d say.

  12. raverbashing · · focus · HN ↗
    Honestly what is &quot;AI generated math&quot;?

    Everything is WFFs all the way down

  13. dsign · · focus · HN ↗
    &gt; However, it is now the case that AI can output mathematical arguments in situations without the human who prompted it being able to understand the arguments, verify them, or take responsibility for them.

    I read this as &quot;anybody can prompt, few can understand&quot;. And &quot;we need more who can understand&quot;. If we had more mathematicians (than we have today) all of them piloting advanced models, the pie would grow. The problem is that AI capabilities drain (by disincentivizing) the education pipeline that would get us those mathematicians, and if recent rumbles about what AI is doing to education are to be believed, it does so many years before students even get to grad school.

    IMHO, it is not that bad. Not having any human who understands linear algebra after the Butlerian Jihad is a win :-) .

    1. octoberfranklin · · focus · HN ↗
      and if recent rumbles about what AI is doing to education are to be believed

      They are.

  14. astaza123 · · focus · HN ↗
    As an answer to AI companies, this is so bad: instead of trying to find a path to a win-win-ish solution with some trade-offs, this says: sorry, we cannot think of any, so just stop making money, will you? Math needs better crisis managers.

    But as an idea, this is even worse: does it mean to stop potential research to cold fusion, cancer and anything as long as it may touch some mathematician&#x27;s interests, or does it mean math is so hopelessly irrelevant that this cannot be the case... Again, as a crisis manager, this is not how you pose it.

    Makes me wonder, were they hired by Sam to sabotage?

  15. ritualdevin · · focus · HN ↗

    [dead]

  16. magus_stoopr · · focus · HN ↗
    basically: &quot;pretty pweez don&#x27;t forget us peeeeple&quot;

    point: imo, the authors have no clue just how psychopathic and broken the execs are for the inc&#x27;s that make these models

  17. bbor · · focus · HN ↗
    Not much to say on the dogfight, but I am yet again pleading for &quot;artificial&quot; as an adjective. Artificial mathematics!
  18. peri-cl · · focus · HN ↗
    In the 18th–19th centuries, what passed for cutting-edge physics was within the financial reach of individuals. Most physics fields today you&#x27;d need a million-dollar lab just to get in the front door.

    Do we mourn the passing of that era? Do we, today, call for the &quot;community&quot; to have &quot;equitable access&quot; to helium dilution refrigerators and electron microscopes and nuclear reactors? Are people calling to outright halt the construction of new physics labs, to bring down the resource barrier of publishable physics, so that everyone may participate equally in the fun?

    This paper is pleading for exceptionalism. If indeed mathematics becomes a field dominated by $15 million agent experiments, then it&#x27;s going to be no different than, literally every other science field. A relentless competition for scarce experimental equipment. There&#x27;s not going to be equitability between the well-funded labs and the not.

  19. globalnode · · focus · HN ↗
    So it seems mathematics is a perfect playground for LLM&#x27;s to show off their abilities. Is this the end of mathematics done by humans? probably.. but that still wont stop some people from going into the field, just like whats happening to computer programming. I find it strange that the two fields LLM&#x27;s are built on are the two its trying hardest to replace humans in. Why will we have to teach mathematics &#x2F; computing to the majority of kids at school anymore if we don&#x27;t need a workforce competent in those skills? Will we just teach kids how to type fast so they can get the prompt in asap?
  20. avazhi · · focus · HN ↗
    Mathematicians surely have copped the biggest L of the AI era - and their transparently self-serving attempts to gatekeep their ivory towery when we now have something that can do it better and faster is, frankly, pathetic.

    Time to get some real jobs, guys. When you&#x27;re asking other entities to slow down with the discoveries so &#x27;real people&#x27; can have their fun, you might not actually be participating in a useful profession.

    This same day will come for other professions like pilots, lawyers, doctors, and teachers, but it&#x27;s funny that the lowest hanging fruit really was what we&#x27;d all most expect lol.

    1. GPerson · · focus · HN ↗
      If you weren’t a complete idiot you’d realize you’re just begging for the end of mathematical understanding and progress.
  21. joeldw · · focus · HN ↗
    Something I&#x27;ve been thinking about that I don&#x27;t quite know how to formalize is the role of _understanding_ in the cycle of progress. The other component would be discovery - generating proofs, creating new algorithms, etc. Discovery pushes the boundaries of a field, but understanding disseminates that knowledge, allowing the field to stand on the shoulders of the new discovery and perhaps make yet another.

    Understanding is really the measure of utility. I suspect that an average human&#x27;s intelligence is similar to one 100 years or even a century ago, and thus our ability to discover new theorems and proofs. The difference is the understanding. We not only have the last thousand years of discovery, but also the compaction, categorization, education, tutorials, etc, that allowed us to learn it effectively in a few years or decades of academia.

    AI is accelerating the discovery part, but the _understanding_ part is just as vital for true progress.

    1. philipwhiuk · · focus · HN ↗
      This is really the Grant Sanderson position - reframe mathematics from proof-search to understanding-distribution.
    2. charcircuit · · focus · HN ↗
      Isn&#x27;t the ability for models to discover new things depend on the model understanding what exists already and figuring out how to apply it? It sounds like we already have everything in place to understand things, prove new things, understand those new things, prove new things with that new understanding, etc.
  22. charcircuit · · focus · HN ↗
    &gt;AI labs that release substantial mathematical output without immediate accompanying human understanding must take responsibility for ensuring that human understanding will follow. In particular, AI labs should provide significant support, including funding, to help develop this understanding.

    This is just reads like asking for a handout. Beyond a Lean proof I don&#x27;t think they are obligated for providing any more interoperability of it. You can already manually go through all the lean statements by hand if you want. Considering how powerful AI proofs are the value of &quot;human understanding&quot; does not seem to be that high. It seems much more valuable to improve AI&#x27;s understanding of math than humans.

    &gt;The use of proprietary internal models by AI labs to do mathematical research risks creating a two-tier system where labs outrun the rest of the field, effectively alienating the mathematical community from its own discipline.

    In such a world it may be worth funding another AI lab who would be willing to sell you access to a powerful model for mathematics. Just because mathematics did frontier math in the past, that doesn&#x27;t mean they are entitled to be at the frontier forever. I would rather advocate for open (to the public) models based off the fact that it allows society to tackle more problems from more angles speeding up the progress of math over than trying to make it about enshrining the previous of class of people into the frontier forever.

    &gt;As for publicly available models, unequal access due to economic and other factors risks establishing a multi-tier hierarchy across the mathematical world and greatly exacerbating existing inequalities that arise from institutional wealth and technological privilege.

    We should not slow the progress of Mathematics down because that might cause inequality. The speed of results coming out should be the number 1 priority here.

  23. __alexs · · focus · HN ↗
    Do the labs have a genuine interest in mathematics beyond generating interesting marketing material?
  24. yuzuquat · · focus · HN ↗
    I&#x27;m curious how this will ultimately pan out. Presently, we scrutinize frontier labs because they&#x27;re the ones able to easily deploy large agent swarms. It&#x27;s not hard to imagine that as costs come down and models become better, smaller and smaller labs&#x2F;organizations will increasingly have this same capability.

    As some back of the envelope math, Openai claimed to have used ~300b output tokens to solve navier-stokes. 4x$200 plans allows me to burn ~2-3b input&#x2F;output tokens a day. What&#x27;s to stop a few highly motivated individuals with a reasonable background in mathematics from spinning up their own massive agent swarms in 6-12 months?

    I think this fragile truce between ai-powered mathematics and overarching mathematical community is just that - fragile. In the same way the stable diffusion broke the dam with the artist community, we&#x27;re seeing the same here.

  25. Chance-Device · · focus · HN ↗
    I think the answer to this is simple: Mathematicians don’t own math. Math is a tool to do useful things. I don’t want this gatekept by people who have a sense of entitlement. And luckily enough, they don’t have any leverage, so the appropriate response is to say no.
    1. lucas_t_a · · focus · HN ↗
      It would be so much work to follow any of this that the answer is guarateed to be a no
    2. hodgehog11 · · focus · HN ↗
      Math is not merely a tool. The question isn&#x27;t one of doing the math, it&#x27;s about publication and release of work. Humans have to follow certain rules, so why should we allow AI labs to behave differently?
      1. Chance-Device · · focus · HN ↗
        Anyone can publish what they want. There’s nothing else to say about it, however anyone may try to pretend otherwise.
        1. hodgehog11 · · focus · HN ↗
          No you can&#x27;t, have you published in top journals before? You can only publish what the community finds valuable, period.
          1. Chance-Device · · focus · HN ↗
            Actually yes, I have my name on a paper in a journal that you’d certainly consider to be top in its field. I’ve also worked in academic publishing.

            You have a very institutionalised idea of what publishing means.

            1. hodgehog11 · · focus · HN ↗
              Care to explain? If a paper is not interesting, it would not get past reviewers. Unless &quot;interesting&quot; is not part of the criteria for entry to the journal? That sounds wonderful if true, but that certainly has never been my experience.

              I feel like I am going crazy, since this is taught in most academic writing courses. Being replicable or persuasive or correct is not enough. It needs to be perceived as valuable, or it will not get through. I learned that the hard way, and found others that taught this message only later.

          2. greiskul · · focus · HN ↗
            Publish whatever you want vs publish in a particular journal.

            You want to publish in a journal you follow their rules. You want to publish something? Go ahead.

            And results are not great results because they are published in top journals. Top journals are top journals because they attract the publication of great results. But the math always speaks for itself.

            1. 11101010010001 · · focus · HN ↗
              Perhaps math speaks for itself, but this is certainly not the case in other fields.
            2. hodgehog11 · · focus · HN ↗
              This is a fantasy I remember hearing in grad school. Get a little more senior and the whole perception shatters. You can put whatever rubbish you want out there. But if you are getting attention, or want attention, you have to play by the rules. Those rules are whatever the community dictates. Otherwise, why would Nick Polson be at risk of being discredited? It&#x27;s no different from any other field, math is not special. Correctness is a necessity. It is not sufficient.
        2. pegasus · · focus · HN ↗
          Really? What about plagiarism? Have you looked into the Navier-Stokes proof? It gets very murky.
          1. erkt · · focus · HN ↗
            Is plagiarism actually illegal? This is primarily an ethical, academic or professional violation.
            1. pegasus · · focus · HN ↗
              Were we discussing legality?
          2. stevenhuang · · focus · HN ↗
            It&#x27;s not that murky anymore. It&#x27;s been determined none of the chat contents were used. If you don&#x27;t believe Anthropic, that&#x27;s your choice.
            1. pegasus · · focus · HN ↗
              &gt; If you don&#x27;t believe OpenAI, that&#x27;s your choice.

              ...and, I would add, it would be an informed choice, wouldn&#x27;t you agree?

              1. stevenhuang · · focus · HN ↗
                You don&#x27;t believe OpenAI given their assessment, so it seems you&#x27;re not operating on evidence in the first place
                1. pegasus · · focus · HN ↗
                  So you just take OpenAI at their word, no questions asked? You imagine them to be unbiased in this matter?
                  1. stevenhuang · · focus · HN ↗
                    At this point it takes some weird epistemics to think they&#x27;d need to outright fabricate the outcome of an investigation when countless other mathematical breakthroughs have been solved the same.

                    They are certainly biased, but I don&#x27;t think such bias is strong enough to cause them to lie about facts. We may agree to disagree here.

      2. AndrewKemendo · · focus · HN ↗
        If a result is replicable that’s the only thing that matters
        1. hodgehog11 · · focus · HN ↗
          Absolutely not. Otherwise, if I prove something original, and it is correct and replicable, this would mean I can publish in Annals of Mathematics. Now if we narrow that to publishing somewhere, then sure, but that&#x27;s irrelevant. This is about values for prominent results (e.g. Annals) for mathematicians.
          1. AndrewKemendo · · focus · HN ↗
            “I can publish in Annals of Mathematics” does not logically follow from “I prove something original, and it is correct”

            Perelman had no publications in annals and didn’t even publish in English or provide every possible proof.

            Your claim is does not stand to even the barest scrutiny

            1. hodgehog11 · · focus · HN ↗
              This was my point though. Not sure why you are disagreeing? The argument was that there was no criteria for publication, or that is how I read it.

              Perelman was already working on an interesting problem, and wrote in ways that were less formal, but still academically sound, so of course he did not need to publish it. What about the people working on problems that are not interesting? You don&#x27;t think they encounter significant difficulties getting their work out there?

        2. pegasus · · focus · HN ↗
          Really? What about plagiarism? Have you looked into the Navier-Stokes proof? It gets very murky.
    3. dannykwells · · focus · HN ↗
      This a thousand times. Thank you.
    4. shank-false-rin · · focus · HN ↗
      That is a strange take. Trying to stop the industry&#x2F;field from becoming a monopoly&#x2F;oligopoly is gatekeep?
      1. pona-a · · focus · HN ↗
        Despite this being a very old man take, as a young person, I think there&#x27;s been a progressive deterioration of collectivist social norms. Everyone feels entitled to do as they please and become offended at the idea they, or someone else they can place their sympathy with, has to temporarily put aside their self-interest and do something for the public interest, be it some arbitrary decorum, regulation, or academic integrity. In a perverse sense of fairness, everybody will cheat their way through life, and find offense in anybody finally being prosecuted for it.
    5. pegasus · · focus · HN ↗
      There&#x27;s plenty of sense of entitlement, yes, but it&#x27;s on the other side. Look at the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.

      Now people ask why AI labs, whose technology is only even possible because of the contribution of the math community, should give a fig about that community. Arrogantly imagining that after having ripped them off, we can just dispose of them. The mind boggles...

    6. GPerson · · focus · HN ↗
      You’re the entitled one. OpenAI steals all the data to train a big model and now you’re angry the people being stolen from want a livelihood.
  26. philipwhiuk · · focus · HN ↗
    Some of this is minor reasonable adjustments, much of it will just be ignored.
  27. onemoreproof · · focus · HN ↗
    I find somewhat funny and interesting the different posts on how the mathematics community should handle AI. I understand this is entirely new, but I do get a feeling that most of these posts &quot;try to control&quot; something that basically cannot be. How the world will use AI for mathematics is not something any small community of mathematicians can decide. It is a bit like trying to define how language should be used, when in practice, it will evolve whether the group want is to or not. For AI in mathematics, the new equilibrium will be build by a &quot;market&quot; of users, each preferring certain bits of using or not using AI. The attempt to formalize and orient this, like a centralized economy, is I believe doomed to failure. That does not mean people should probably share how they see it for themselves.
    1. hodgehog11 · · focus · HN ↗
      It is not deciding control, it is determining agreed values in policy form. At least, that is how I see it.
    2. GPerson · · focus · HN ↗
      The world != OpenAI. Please at least try to engage with the topic before weighing in.
  28. keybored · · focus · HN ↗
    Let’s see who HN now thinks are selfishly standing in the way of the democratizing force of Big Tech: mathematicians.
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