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If math is more than proof, we need to better celebrate the rest of it

433 points · 285 comments · num42

  1. youoy · · focus · HN ↗
    Part of the controversy here is that now the skill advantage that some Field Medalist had is much narrower. The fact that fields medals have an age limit implies that it favors brain power over understanding. And that was the guiding light award of the community. So i find it "funny" (and natural) when they are offended by AI. That is the main "crisis" of mathematics.

    In my opinion there has never been a better time to be a mathematitian, and there has never been a better time to be a software builder.

    But there has never been a worst time to have the need to prove your economic value as a mathematitian or software developer alone. Because "understanding" is not something you can prove in one afternoon, its something that you prove with a life.

    1. sweezyjeezy · · focus · HN ↗
      > In my opinion there has never been a better time to be a mathemetician...

      As an ex-mathematician I assure you this is very wrong, and every working mathematician I know right now is completely miserable, and/or trying to flee the field as fast as possible. It's like telling a chair-maker during the industrial revolution that there had never been a better time for them, since now they could operate chair-making machines instead of toiling away at the wood themselves. It assumes that they were purely in it for their passion for mass-producing chairs. The majority of mathematicians get into the field because they love problem solving, and the gauntlet thrown down by challenging math tasks.

      Many parts of this will never be useful for society on a grander scale - but this is reflected in the finances - pure math is closer in funding-terms to a humanity than to hard science. Now even this is _massively_ under threat, and Tao and co need to pivot quickly to stop this from becoming a bloodbath.

      1. soVeryTired · · focus · HN ↗
        Probably true for the dedicated problem solvers (of which Tao is one IMO). But I doubt there's ever been a better time to be a theory builder (more like Peter Scholze, or Grothendieck).

        Some up with an idea and leave the system to check it 15 different ways, and see whether you can simplify an existing body of theory. It'd be like having an army of lightning-fast grad students.

        1. sweezyjeezy · · focus · HN ↗
          I'd even say Scholze is not a great example here. Most of the work he's known for is progression towards the Langlands program - which is very much a problem to be solved, and one I would imagine he'd not be thrilled for an AI to one-shot. I agree that it is somewhat 'up the chain', in the same way that software engineering has not immediately disappeared now that performing coding tasks is largely automatable.

          But I also take issue with 'never been a better time' - e.g. is this really the greatest time to be a software engineer? Everyone has AI psychosis and feels like they're a couple of breakthroughs away from being unemployable. The same is even more true in math - we've gone from failing IMO problem 6 last year, to solving NS. The rate of change is formidable, it feels like there may not be many places to hide in a few years.

        2. nilkn · · focus · HN ↗
          This is coming next. There's nothing particularly special about theory building. Successful theory building is always oriented towards solving a problem, because otherwise even humans can easily spam out a bunch of nonsense. This is a real problem that the math community has experienced on multiple occasions pre-AI. I'd go further and say that theory building is irrelevant if it doesn't help solve problems people care about.
      2. youoy · · focus · HN ↗
        Im an ex mathematitian too. And if i was in academia I would probably have the same reaction. Thats what i say that its the worst time for proving economic value.

        But if you are in for theory building and understanding, then you are not constrained anymore by your motivation to grind through countless hours of formal theorem proving. And you do not need to have superhuman formal manipulation skills and memory.

        For me mathematics is not the formal system, so LLMs will never be able to do end to end maths.

        1. lapinot · · focus · HN ↗
          The practice of "theory building" is especially endangered by the current LLM uptake. Not because LLMs are good at it, because they are bad at it. Worse, they sometimes actively hinder theory building, because it usually rests on actually having deep experience with some techniques: 1: you do something over and over, 2: it becomes a second nature, you just get the feel for it, 3: you intellectualize this intuitive understanding, 4: you discover a new structure, or a better way to express/teach/learn/use an existing one.

          Theory building was always kind of niche, or at least less prestigious (in comparison with solving well-known problems). Now, because the mad problem solvers are pulling on the blanket so much harder, the marginalization is getting worse.

      3. calf · · focus · HN ↗
        But these are not very good arguments, because it makes it about the fall of institutions (the funding) and people being miserable for personal reasons rather than prosocial reasons. Tao here clearly suggests that math is not reducible to "problem solving" or "proofs", the valuable part is much more than that framing.

        The concerning argument about the status of math would be an outline that it will get destroyed by a process of societal atrophy and there is no turning back, and the AI powers are not a good substitute or replacement for it. If an entire society becomes reliant on these oracle machines then it would be analogous to children never learning arithmetic because they were handed calculators. How could the human race still flourish? We would anthropologically regress. We'd be little better than animals, like the Borg zombies.

        That is a much more profound threat than people worrying about their own careers or faculties disappearing like the humanities. This is a serious anthropological reckoning.

        If math experts are that freaked out already then basically all of science is soon to follow, decade by decade. "Singularity" comes to mind.

        1. sweezyjeezy · · focus · HN ↗
          Broadly I agree with this, but I was refuting the statement "there has never been a better time to be a mathematician". You are changing the question to something different here, and using it to say my argument is bad.

          I think math is a microcosm for "thought-work" in general. We have been in a symbiotic relationship with capitalism for decades now, where the hope of a well-paid white collar career encourages people to spend time and money to enrich themselves through education. The proliferation of AI cheating at college already signals that employment is the primary goal over intellectual growth, so one imagines this governs what happens next if labor demand disappears.

          It's hard to say where this all leads, but I have very low optimism for higher-level math understanding being something that humans value in the same way in the coming decades.

        2. bonoboTP · · focus · HN ↗
          The post is not by Tao but by Grant Sanderson, maker of the 3blue1brown YouTube channel.
      4. trostaft · · focus · HN ↗
        > As an ex-mathematician I assure you this is very wrong, and every working mathematician I know right now is completely miserable, and/or trying to flee the field as fast as possible.

        To throw a counterpoint to this into the writhing cesspit of HN, I'm active in academic mathematics (postdoc) and every one of my collaborators is deeply in love with the field and their jobs. Perhaps the grass is greener on the applied mathematics side of the fence.

        1. D-Machine · · focus · HN ↗
          IMO this would track, applied mathematics (even e.g. data science, though perhaps calling that applied math is a bit generous / insulting to more serious applied math) is in some ways more exciting now because it is far easier to surface complex / appropriate methods for the task at hand, and you can more confidently explore these methods because the AI sort of "has your back" in catching some of the more obvious beginner errors you make during these explorations. Plus, applied math feels roughly more results- than process-focused, compared to pure math.

          IMO the divide here between pure vs. applied math feels a lot like the divide between those who enjoyed coding for the understanding it led to, i.e. the writing itself was the joy, vs. those that primarily coded for the results. I enjoy the creative part of coding, the thought of software jobs just devolving into writing specifications and doing code review very much kills it for me.

    2. elendilm · · focus · HN ↗
      Spot on. I agree. There has never been a better time to be a software builder or a mathematician.

      Seekers whose primary motive is validation instead of understanding are the ones who are getting paranoid.

      Thoroughly enjoyed your thoughts. The age limit is a joke if what you care about is true understanding.

    3. ceh123 · · focus · HN ↗
      > In my opinion there has never been a better time to be a mathematitian

      I think it’s a great time to be a curious mathematician, especially in a niche field where you’re not competing with hundreds of agents of the best unreleased frontier models.

      However it’s a very scary time to be a professional mathematician because publish or perish is going to cause a race to the bottom for cranking out results as fast as AI can let you. [0]

      [0] <a href="https:&#x2F;&#x2F;ev12183725.substack.com&#x2F;p&#x2F;a-highly-productive-dark-age" rel="nofollow">https:&#x2F;&#x2F;ev12183725.substack.com&#x2F;p&#x2F;a-highly-productive-dark-a...

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