Thread

The Advisory Group on Mathematics and Artificial Intelligence

162 points · 87 comments · digital55

ipdashc · 1790020558 · focus · HN ↗
I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
They might be the first community I've seen to experience the AI "rush" and (at least as presented to an outside observer) immediately come together, assess the situation, and calmly, empathetically, and rationally act. They evaluated what AI is good at and what it lacks. They've thought through how it'll likely affect their field in the future. They've explained where the need for humans still lies, and made clear proposals for how to change their own field and for what demands to make of AI companies. Of course they're not all on the same page, but they're at least talking and trying.
They haven't started worshipping the machine god and loudly claiming their whole field is solved. Nor have they flailed wildly at LLMs as if complaining enough about it will make them go away.
Every major statement I've seen come out of the math community on this matter reads as well thought-through, humble, reasoned, and deeply human.
In these days of fear, uncertainty, and obsolescence anxiety, honestly, they've given me some confidence that maybe we will figure this stuff out after all. Maybe we'll learn from them. Who knows.
1. ksd482 · 1790020937 · focus · HN ↗
  Agreed.
  Their field is extremely rigorous. As rigorous as it can possibly get in that they have to prove each and every line of their work beyond any doubt. The discipline they have cultivated in their culture shows in their response to AI as well.
  As opposed to some other fields in which rigor was either not part of the culture or was not always possible. For e.g., software engineering in terms of code quality being produced. There were some indirect signals here and there but they are all subjective.
  1. cubefox · 1790088307 · focus · HN ↗
    In some sense software engineering is more rigorous than mathematics, because proofs are generally informal, apart from those written in Lean, while all computer programs are strictly formal, as otherwise they wouldn't be machine-readable.
    ksd482 · 1790187862 · focus · HN ↗
    I see what you are sayings. That's an interesting point of view.
    Perhaps we should define what rigor means.
    Your point is that code is executable and speaks for itself whereas a Math proof (non-lean) is just someone's writing on a piece of paper.
    Now let's compare the "practice" of doing Math and software engineering. In Math, every step is very intentional, and getting to a point where a proof is complete and correct is a very long, laborious, difficult and intentional process. Not to mention, the work is also peer reviewed (for published stuff). This is what I mean by rigor.
    In software engineering, the practice is quite different. We defined the problem (somewhat), come up with a design that we "think" would work, write programs that we think is correct and then execute it. Most of the time it doesn't work exactly as we would have predicted. So we take the signal and adjust. So it's a more iterative part and this gets us closer to reality (what we actually want it to be), step by step.
    So comparing the two, the major difference I see is in one each and every step is very intentional and we can't guess it. While in the other one we have lots of liberties, but we are still making progress.
    So to me the difference is just between the practices followed in the field when it comes to rigor.
    cubefox · 1790196848 · focus · HN ↗
    Maybe a similar comparison would be this: for proofs, the standards of correctness are purely internal and can in principle be formally defined, as in Lean. The formal conjecture has to follow from the premises. Either it is proven or not. In contrast, in 99% of ordinary software, no fully formal standard of correctness exists. The requirements are informal. So what counts as a bug and what doesn't is a judgement call that can only be checked by asking the person who wanted the software whether it works as intended.
2. bamb008 · 1790021079 · focus · HN ↗
  >Every major statement I've seen come out of the math community on this matter reads as well thought-through, humble, reasoned, and deeply human.
  Can't disagree with "deeply human", but I wouldn't always use it in a positive sense:
  <a href="https://proofsandprompts.com/2026/09/10/open-letter-about-the-mathathon/" rel="nofollow">https://proofsandprompts.com/2026/09/10/open-letter-about-th...
  >Participation in an event so closely associated with Anthropic and OpenAI could plausibly negatively impact the future reputations of participants
  1. antonvs · 1790060926 · focus · HN ↗
    What do you believe doesn’t reflect positively on the authors of that open letter? It raises valid concerns, and the statement you quoted is a factual observation.
    p-e-w · 1790068247 · focus · HN ↗
    It reads as a transparent attempt at intimidation to me.
    antonvs · 1790194809 · focus · HN ↗
    It’s a true statement. The way you perceive it is in your mind, not a property of the statement itself.
    p-e-w · 1790228347 · focus · HN ↗
    “If you testify tomorrow, you may not live to see the end of the day. It’s a true statement…”
  2. neuroticnews25 · 1790073405 · focus · HN ↗
    Wow, that's disgusting.
3. bananaflag · 1790021487 · focus · HN ↗
  > I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
  As a mathematician, I am a bit disappointed by my (admittedly illustrious) colleagues.
  I get the need to take it slowly (and I am a quite impatient person, so I shouldn't get to decide stuff like this), but everything said feels a bit too sour grapes for my taste.
  Ok, maybe AI did not solve the field (I believe it will, btw), maybe there is a need for human "understanding", but:
  1) They don't seem to consider even the possibility (not the certainty) that they might be wrong, that math as we know it is gone, and we cannot "adapt"
  2) They seem to have been oblivious all these years about AI eventually reaching this point (at least I personally wasn't, I predicted this stage back in 2018)
  1. traes · 1790022482 · focus · HN ↗
    Regarding 1, it's not clear what you want them to actually do. Would you rather they just gave up, rolled over and died instead of at least trying to rescue their field? What is to be gained from considering this?
    besterman23 · 1790024597 · focus · HN ↗
    I suppose you could say, hypothetically, that if the field were “solved” then the protection of the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide.
    The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
    ImPostingOnHN · 1790026620 · focus · HN ↗
    > The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
    They aren't in the way. AI labs can do their own math all they want, and nobody is stopping them. Rather, mathematicians are simply speaking about the topic.
    So is the answer that they should just shut up?
    p-e-w · 1790068031 · focus · HN ↗
    They absolutely are in the way. We’ve had the most exciting months of mathematical progress since antiquity, and the vast majority of voices from mathematicians have been bitching about one thing or the other, to the extent that they now got themselves a committee that (co-)decides when, how, and possibly if, the next batch of results is made available to the public.
    Ar-Curunir · 1790080746 · focus · HN ↗
    Please. Have you been doing mathematics ? Yes, some big open problems are solved. I have not seen the ideas therein used to solve related or other problems. That is the point of most mathematics: to develop frameworks and general techniques for understanding and solving problems, not solving one-off problems.
    For example, group theory lead to a useful way of thinking about how to solve a wide array of problems. That is what mathematicians are seeking.
    ImPostingOnHN · 1790121798 · focus · HN ↗
    People merely speaking their mind does not constitute getting in the way.
    I'm sorry that you personally don't like that mathematicians are "bitching" about OpenAI snaking their work out from under them, and would like to silence them. But if we're going for consistency's sake, maybe consider taking your own advice here before giving it to others.
    In the meantime, OpenAI can do whatever they want, mathematically-speaking. Nobody is in their way. If there isn't further meaningful progress from them, that would seem to strengthen the work-product-theft hypothesis.
    joe_the_user · 1790026863 · focus · HN ↗
    If LLMs could both prove any relevant theorem, explain such a theorem cogently and lay the groundwork for further theory, I don't see how any way mathematicians could stand in the way of that.
    breuleux · 1790085608 · focus · HN ↗
    > the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide
    Wiping out an occupation that people enjoy and that gives them purpose (making them "obsolete") is a public mental health crisis, if anything. It's unclear that the "benefits" of the "solved" field actually outweigh that.
  2. 7ahGa · 1790025542 · focus · HN ↗
    As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years and now do damage control by nudging everyone to either hypothetical open models paid for by industry or the EU or sitting in a committee that "advises" OpenAI.
    No one is saying "Perelman and Wiles didn't need that silly AI and N-S was more of a counterexample". Most people imagine the sky is falling.
    What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
    bananaflag · 1790025931 · focus · HN ↗
    > As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years
    I did notice, this is why I had thought that they had thought through the consequences. But, unfortunately, it is likely they imagined that AI would plateau somewhere around the "smart undergraduate" level and that they will stay relevant in pure problem solving.
    creato · 1790046051 · focus · HN ↗
    Was there really a choice? What they do or advised others to do would have had no bearing on what is happening.
    oliculipolicula · 1790050359 · focus · HN ↗
    And why have the Nobel Prize winners been silent (or taken post-Nobel bets contrary to the current consensus ie Hinton-Hassabis)?
    Taking GP at his word, I'd be more terrified if Oai had identified one hundred NEW open problems..
    In contrast with Fields Medallists, some Nobelists get the prize for something they'd eventually NOT be (in)famous for. Like Josephson. In hindsight, will it be because they found out, as young unknowns, how to explore underappreciated avenues without millions in dedicated funds (uh encouragement).. ??
    GP, did you? Get the prize for the question you are most proud of.
    torginus · 1790056740 · focus · HN ↗
    > What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
    Which is what I think a large chunk of AI progress actually is - people taking the latest models out for a spin, and browbeating them to actually ship code, and RLHFing them to ship better code in the process, either directly or indirectly through Github.
  3. Davidzheng · 1790029590 · focus · HN ↗
    I think I'm mostly on your side (also I believed early it would get here), but what does it mean to "solve the field"? I'm pretty much as bullish as you get on AI but I'm sure I can come up with questions AI cannot solve. I think the space of problems in math is so large and the distribution of proof lengths so heavy-tailed, there's probably no way without dyson-sphereing the sun to solve all easy to state problems.
  4. huurtehoog · 1790041863 · focus · HN ↗
    How do you conceptualize mathematics being 'solved' and 'gone'?
    How do you reconcile that with incompleteness and undecidability results?
  5. runsWphotons · 1790044605 · focus · HN ↗
    I think it is good people are talking but there seems to be a lot of "forced optimism", especially by people obviously hoping to keep a channel open between themselves and the labs.
    I think it isn't true that no one imminent is considering (1). Tsimmerman said he thought the job of math researcher was over as soon as he announced he was leaving the field.
    I think the question is so far still open, but it is easy to imagine Tsimmerman was right. I haven't been impressed with the calls for "human understanding" as the really important thing. It seems to miss the point of why math has been funded (not exactly problems, but certainly not to ensure every theorem is understood either).
    As a scifi comment, it is now possible to start thinking about some future AI system which decides if it will need to explain certain math to humans and to pick and train young people for that purpose.
  6. redf5 · 1790062911 · focus · HN ↗
    Without understanding, what are we?
4. FLeXMurphy · 1790023797 · focus · HN ↗
  > They haven't started worshipping the machine god and loudly claiming their whole field is solved.
  Don't give Dario any ideas please.
  > next week: Mathematicians are solved [214 points, 891 comments]
5. stuckinhell · 1790025079 · focus · HN ↗
  No, I don't think they are adapting well. I've seen 3d designer at my company adapting better on the disruption and paradigm shifts GPT-6 Astra is going to cause.
  The 3D designers are in a tougher situation because it's far less of abstract issue then math, and yet the results are astounding. It's hard to believe until you see it yourself. It's surreal.
6. svat · 1790033640 · focus · HN ↗
  Every community approaches problems with the tools at its disposal. Doing mathematics is about thinking, so mathematicians approach problems (at least in public) with more thinking and less emotion (than some fields where emotion is much more important). While you and I may appreciate this approach (and even be inspired by it), it remains to be seen whether it ultimately makes the outcomes any better.
7. keeda · 1790035300 · focus · HN ↗
  I would not attribute this attitude to the entire Math community, there clearly are many who are reacting negatively to this, as evidenced by several comments on various forums including this one. People are understandably upset about their chosen profession and livelihood being upended and reacting accordingly, similar to how people from other impacted professions are.
  This group of Mathematicians just happens to be more willing to accept the inevitable and adapt. I would actually say software engineers, being amongst the earliest impacted by AI after creatives, clearly have adapted to the new reality much more broadly as evidenced by online discourse and coding agent providers' skyrocketing revenues.
  1. rocqua · 1790049430 · focus · HN ↗
    Presumably OP believes that software engineers went to far in the direction of “started worshipping the machine god and loudly claiming their whole field is solved.” Certainly within software engineering there is much louder voices on that side of things. By now the voices saying that it’s useless have pretty much died out. But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
    One might argue that this is due to size of the software community, or commercial interests. But I do believe OP was right in his description of the response of the math community as different from the software community.
    keeda · 1790065460 · focus · HN ↗
    > But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
    But my point is the wider Mathematics community didn't do that either. We are just looking at the subset in TFA and assuming they represent the whole community. If you look at AI + Math-related articles and threads on HN you'll definitely see a lot of consternation from Mathematicians.
    ipdashc · 1790082554 · focus · HN ↗
    It's entertaining to me that so far you're one of the only replies to notice this :)
8. deterministic · 1790054791 · focus · HN ↗
  I disagree. Software developers seem to have adapted to AI much faster than the maths community.
  There are certainly still strong opponents of AI, but they seem to be a small, vocal minority. Most developers seem to have simply adapted and moved on.
  1. feanaro · 1790068191 · focus · HN ↗
    It's possible and I dare say even likely that you are missing nuance and observing bias from your bubble. It's possible to avoid being an AI "opponent" while still being a sceptic. It's possible to use AI reluctantly and with tact instead of going all in.
    The whole thing is far from over when we haven't experienced the worst of the technology yet: deskilling, concentration of power, extreme imbalance of wealth, military and surveillance uses, etc.
    deterministic · 1790210520 · focus · HN ↗
    > I dare say even likely that you are missing nuance and observing bias from your bubble
    I hope you’re not assuming you’re immune to being in a biased bubble yourself.
    I’m just honestly sharing my experience. Obviously, your experience has been different, but both experiences can be true at the same time.
    feanaro · 1790243908 · focus · HN ↗
    Of course, sorry if that came across as more combative than necessary. I was trying to point out two things I guess:
    1. "Your experience is not universal from my perspective, and I offer my experience as evidence"
    2. The possibility that this adaptation you are observing is neither a stable equilibrium given future developments, nor is necessarily an indication that the people using AI have bought into it fully. I use AI heavily while remaining a sceptic.
    deterministic · 1790298874 · focus · HN ↗
    Hey, no problem, and thanks for the level-headed response. We need more of that in this world.
    And yes, I agree that we still don’t know the long-term consequences of AI. But current LLMs are nowhere near good enough at judgment or new ideas to replace most jobs.
    I expect they’ll mainly automate parts of jobs rather than replace them entirely. That’s exactly what I’m seeing as a software developer. I use an LLM to write my code, but it only works well when I apply good judgment and shape the context and prompts to remove ambiguity and then carefully review the results.
9. canjobear · 1790103083 · focus · HN ↗
  > Nor have they flailed wildly at LLMs as if complaining enough about it will make them go away.
  If you look at the comments on the blog post, you'll find plenty of this.

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