We're gonna need a lot more mathematicians

(terrytao.wordpress.com)

42 points | by srcreigh 2 hours ago

8 comments

  • pyridines 9 minutes ago
    > Before approving construction, I would want communities of humans to understand why the design works and what justifies confidence in its safety. I would hope that we all would.

    Until very recently, I pored over every single line of code Claude generated with razor sharp scrutiny. I would usually catch issues with every response. I'm catching fewer problems these days. Maybe the model is just getting better, and maybe I'm being less careful while under pressure to ship more and more often. But model capability is obviously growing. Even back in March, you could tell it "give me a function that adds two numbers" and you could be 100% confident that it would write the correct function. There was almost no point in looking at the code. Since then, the complexity floor of problems in the category "this is so simple that the model couldn't possibly get it wrong" is rising, and with it, my cognitive surrender to the model is increasing too. Why check it? It's obviously going to be correct.

    If AI designs a terawatt fusion plant, then of course we're going to meticulously pore over every detail to ensure safety, reliability, efficiency, whatever. If we find no flaws in the design whatsoever, will we be less careful about the second one? The third one? What about the ten thousandth one? Will "a nuclear fusion plant" become something that models couldn't possibly get wrong?

    Terence Tao is arguing that the human involvement in research is crucial, but doesn't convincingly justify why, in my opinion. He says that "human agency is a value of fundamental importance" and that we will need to build "thriving human communities that can understand [AI ideas] together" - not for the sake of correctness, which AI may surpass us on, but for, I guess, the possibility of reclaiming human meaning and purpose. I don't disagree with this at all, but it's not an argument, it's a statement of values. Unfortunately, the stark reality is that if AI does surpass humans, it will become the economically dominant strategy to not verify them and not double check them, but to just do whatever they say. This seems like a great way to raise p(doom). But as the models get better and better, and as I'm scrutinizing Claude's output less and less... I just hope that there are more Terence Taos out there than people like me.

  • siavosh 59 minutes ago
    Like most of us I go back and forth between sheer optimism and fear for the future that AI may usher in. Recently I started vibe coding a fun video game with my ten year old. The experience is different than my work because it’s been such a joy to basically have a personal genie in a bottle help me make some personal art with a loved one regardless of either of our skill sets. The concept the author of this post is arguing now resonates with me more than it would have a few weeks ago. The sheer surface area that AI can create in our intellectual life is limitless and needs humans to explore. There can never be enough of us in that sense. Whether it’s as validators or creators.
    • demibabs 28 minutes ago
      Certainly humans can enjoy exploring such things, but will they really be needed?
      • dozerly 22 minutes ago
        What does needed even mean? To produce shareholder value? Maybe not. To explore thoughts and ideas humans have for fun? Certainly
        • awepofiwaop 21 minutes ago
          To make money in order to eat food and have a home.
          • delis-thumbs-7e 1 minute ago
            We could feed the whole population of the world if we decided to, we definitely have enough production[1]. If we pretend AI-assisted automation can do most work - which still currently is an highly dubious claim - we could just provide food and shelter for free to everyone, if we so desired. It would require quite a lot of restructuring and dietary changes, but it is possible.

            [1]https://online.ucpress.edu/elementa/article/doi/10.1525/elem...

          • siavosh 13 minutes ago
            If AI leads to an era of abundance, then the economic system has to change. The system it transitions to and what that transition looks like will need to be fought for, and I imagine it’ll be done better in some places than others. Yet I think the parallel existential question of meaning in this world is one that is inherently optimistic. Humans decide meaning, it is not something imposed on us or taken away by the existence of something else.
            • greesil 5 minutes ago
              Right now that looks like a bunch of rich edgelords and us as serfs
          • RealityVoid 16 minutes ago
            The current approach to resource distribution worked so far. When it stops working because we have too much abundance, we'll settle on another one.

            That doesn't mean the transition will be smooth. It doesn't mean that certain classes won't be worse off. I can certainly imagine programmers being among the losers. And there certainly are futures where we slide in dystopia. So let's try building the good futures. Alea iacta est.

          • inopinatus 17 minutes ago
            Money will become unnecessary. The future Anthro Park will no doubt provide a safe enclosure, feeding at regular intervals, and an enriching environment for you and your fellow semi-evolved simians.
  • zfnmxt 1 minute ago
    One of the reasons that AI feels so ominous to me is that it threatens (and exposes) my approach to work. I never enjoyed reading papers and always had great difficulty efficiently crafting a broad but pragmatic & useful understanding of a problem and its context (especially related problems that have been addressed in other works).

    My approach to research was just to spend (human) tokens---play with the problem long enough, spend enough cycles, and eventually figure something out.

    Amit says that struggle is essential to understanding---of course I agree---but it's not sufficient. Depth accumulates one problem at a time and breadth only follows if you solve a lot of problems; that works great in school where problems take minutes to hours and span a large breadth of areas, but isn't a great strategy in research where problems take months to years (at least if your approach is just to play with the problems from first principles, as mine basically is, and your ultimate goal is to forge expertise).

    I have not worked on a lot of problems in my research career (maybe five or six). And despite my PhD, I consider myself no expert. And it's doubly bad when you have software that can largely structurally emulate the same process that I use for research (although, so far, AI has been unable to solve the novel problems I've worked on (at least with my plebeian Claude subscription)). I've really been mourning this lately because I enjoy just obsessing about a problem and just toying with it, but now I have to confront that it really is a bad long term strategy in terms of personal development.

    I think the path to survival and flourishing in this nascent AI world is expertise that is deep and broad, precisely so---as Amit points out---we can understand (and evaluate) the solutions that future AIs propose. I suggest an amended title: we're gonna need a lot more experts.

  • bluejay2387 16 minutes ago
    "I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs. " -- I can't be the only one who thought about the scene where the scientists ask Deep Thought the ultimate question...
  • inopinatus 37 minutes ago
    > Imagine that a future AI system proposes a radically new design for a one terawatt nuclear fusion power plant

    This is an unfortunate example to choose, being as it is entirely confounded by the canonical illustration of the https://en.wikipedia.org/wiki/Law_of_triviality.

  • macrolocal 35 minutes ago
    Russell once remarked that all of mathematics would be trivial to a sufficiently intelligent being. It builds conceptual tools for limited minds, that lets them understand far beyond their natural reach.

    In a world with ASI, having that capacity is vital.

  • atleastoptimal 44 minutes ago
    It would be nice to have more mathematicians, but we don't need more. Once AI math goes so far beyond human abilities, any human involvement is like an ant trying to understand quantum physics
    • jahbrewski 36 minutes ago
      Even if that happens, what’s the point if there’s no human involvement? AI doing math for math’s sake? And doing what with it?
      • rudy6912 20 minutes ago
        > AI doing math for math's sake?

        Yes, why not? And, of course, AI doing math for AI.

        We may not be needed forever...

      • alex_sf 26 minutes ago
        I don't understand how to make a modern CPU. I'm not involved in the manufacturing of it. From my perspective, there may as well not be any human involvement. I can still use the resulting chip (in an larger system of other things I can't make and wasn't involved in) to argue with you on the internet.

        It becomes another abstraction, really. As long as we can use it for something useful, it's still valuable.

        • awepofiwaop 19 minutes ago
          At some level of abstraction it's all built around allowing you to do some work/play/etc that you understand. Some of that work allows you to make money and eat food.

          If the LLM is operating at such a high level that it never actually constructs a useful product for humans to use, then how will that be good for humanity?

    • chadcmulligan 35 minutes ago
      There was this old TV series 'Fame' when I was a kid, there was a piano player that was at the school, he didn't want to perform though - he just wanted to play the most intricate complex music, the professor rightly pointed out what good is music if no one else can her it. Isn't AI math the same (assuming it gets to this point, yet to be proved) what good is it if no one can use it - just the AI's showing off to each other, if that does happen we'll need more mathematicians to show the rest of us what they're going on about. I find it an exciting time, imagine if we can accelerate a few hundred years into 20, wow, the one problem is capitalism won't work, so sad, we'll figure out something else.
    • gaigalas 27 minutes ago
      Need? We don't need lots of things, including computers. We did well without them for hundreds of thousands of years.

      We want to understand. Quantum physics, mathematics, how stuff works. Ants don't.

      That want is not a given, not all of us have that drive. In fact, very few of us have it. So far though, it seems multiple disconnected civilizations learned to keep that trait going instead of suppressing it and focusing only on practical ant-like activities.

    • rvz 37 minutes ago
      > Once AI math goes so far beyond human abilities, any human involvement is like an ant trying to understand quantum physics

      This makes no sense whatsoever.

      We need more, because there will always be far more difficult problems yet to be discovered and solved, and that means, we certainly need expert humans to define and verify them.

      If you cannot even explain the problem you are facing, not only you don't understand it, but you certainly would not be able to know if the AI solved your problem correctly.

      • WarmWash 35 minutes ago
        >and that means we need expert humans to define and verify them.

        And this will be true for how long? 3-4 months?

        • rvz 30 minutes ago
          As long as there are problems to discover and solve, which is forever.

          The risk of liability is a social problem that is far more difficult to be solved with technical solutions even with AI.

  • algorithm314 26 minutes ago
    Life is all about tradeoffs. Mathematics have no tradeoffs. We need more engineers.
    • inopinatus 23 minutes ago
      Life is all about purpose. Mathematicians are instead concerned with meaning. We need more philosophers.