We're gonna need a lot more mathematicians

(terrytao.wordpress.com)

73 points | by srcreigh 3 hours ago

14 comments

  • pyridines 1 hour 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.

    • breuleux 41 minutes ago
      > What about the ten thousandth one? Will "a nuclear fusion plant" become something that models couldn't possibly get wrong?

      For what it's worth, ten thousand terawatt fusion plants probably approaches the level at which the sheer intensity of energy production would cause significant disruption to the climate (it's roughly 5% of the Earth's entire solar input). Every energy source becomes dirty past a certain point. It would be wiser to learn how to build a utopia within a limited energy budget than find a way to produce enough of it to cook the damn planet, but who am I kidding, we're going to build a million of these things.

      • itishappy 39 minutes ago
        This assumes we're still building them on Earth.
        • breuleux 17 minutes ago
          Why would we have stopped?
    • xtracto 1 hour ago
      Imagine the first time electric calculators calculated the square root of 5. I'm sure people would verify again and again if what the circuits calculated was right.

      Then in the 80s, you presses 2 buttons and there you had it in your classroom without thinking twice if the electricity arrived correctly at the transistors.

      How crazy will the world be once our [current gen] ANN are like that!

      What an amazing thought.

      • delis-thumbs-7e 35 minutes ago
        Calculators and computers are deterministic, they give the same output to the same output every time. Language models specifically are not. So it might give you are function that is correct, or a function that is not, or worse yet a function that behaves correctly, but introduces some god-awful bug down the line that can cause serious havoc. It is obvious that they need supervision, not only for output, but also sandboxing and various harnesses for them to not do any “oops, I deleted your codebase sry” kind of nonsense people post to Reddit.

        So I think the problem is to determine which problems under what instructions we can safely give to a model application to solve and how we test the output for safety and functionality. This would create more usable and safe, albeit a bit more boring, AI-based applications alin to a calculator or general computer. Whether this is posswith current model architecture is another thing.

        • raincole 23 minutes ago
          > Calculators and computers are deterministic

          How do you know?

          Memory bits flip randomly. It's not a super rare thing either. You and me have experienced that many times without knowing. The only reason that computers feel deterministic is that we have error-correcting code to fix that. But in the most extreme cases, when multiple bits flip together, once "deterministic" program can generate unexpected output.

          So why do you trust computers? Because statistically the case is just very unlikely. Therefore if AI is statistically unlikely to make mistakes there is no reason to not trust them.

        • zjjsjsjjs 12 minutes ago
          [dead]
      • itishappy 42 minutes ago
        Calculators hallucinate! Mine did not come with error correcting RAM. (Though you might not know from the price.)
      • vinyl7 1 hour ago
        Given the disappointing levels of intellectual decay that our current technology has thrust upon civilization, I only see humans reverting back to neanderthal levels of intelligence in short time with the advent of AI
        • Seattle3503 59 minutes ago
          > One wonders whether a generation that demands instant satisfaction of all its needs and instant solution of the world's problems will produce anything of lasting value. Such a generation, even when equipped with the most modern technology, will be essentially primitive — it will stand in awe of nature, and submit to the tutelage of medicine men.

          - Eric Hoffer

          • ares623 46 minutes ago
            > Sounds awesome

            - Tech Bro

        • nradov 45 minutes ago
          There's no reliable evidence that Neanderthals were less intelligent than modern humans. They're extinct now (except for a tiny genetic legacy in some human populations) but that could have happened for a variety of reasons unrelated to intelligence or lack thereof.
        • genxy 41 minutes ago
          > neanderthal levels of intelligence

          were gonna need a citation on this one.

    • etrautmann 1 hour ago
      Nit, but Terrence Tao did not write this article, it’s a guest post.
    • vatsachak 3 minutes ago
      The models get things wrong in the way that humans don't.

      They will never make a logical error yet make terrible assumptions and poor long scale decisions.

      Wake me up when an agent swarm can write gcc in a box sealed from the internet.

    • card_zero 46 minutes ago
      You oppose correctness to meaning and purpose, which you seem to imply are impractical values. (Worthless values, then?) But you don't mention creativity. The article blithely says that AI creates new ideas and understands things. I don't think it does.
    • charcircuit 7 minutes ago
      >the economically dominant strategy to not verify them and not double check them

      In the big scheme of things is it really that expensive to verify it if a lean proof is generated? The agent itself will likely have already verified it before calling it "done".

    • LoganDark 1 hour ago
      The more likely AI becomes to produce working code every time, the more likely it will become that a one-in-a-thousand or one-in-a-million error goes unnoticed at generation time. It sucks.
      • ipsod 1 hour ago
        Bugs have existed since before AI, though. It's remarkable how bad a lot of very successful software has always been.
      • MattGaiser 1 hour ago
        Sure, but we currently find that acceptable. Codebases are full of such bugs.
  • Animats 17 minutes ago
    "We’re gonna need a lot more mathematicians."

    What the article really says is that we're going to need much smarter mathematicians. That is not possible for puny meat-brain humans. Humans are close to their ceiling. AIs are just getting started.

    In practice, we're probably going to hit that limit first in IC design. I once went to a talk by the Intel engineering manager who headed the Pentium Pro effort. That was the first superscalar x86 CPU, and it took about 5,000 engineers at peak to design it. Getting that many people coordinated on one thing was a real achievement. Then Intel stayed with minor tweaks on that design for years.

    We're soon going to be seeing designs of even greater complexity cranked out by AIs. No human will understand them at the gate level. Reading AI-written programming language code is bad enough. Reading AI-written Verilog may be beyond human comprehension, except in small sections.

  • metalspot 32 minutes ago
    There is a failure to understand that the process is the result. You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind. The output of an LLM is useless without a human mind to comprehend it. We can have Super Intelligence, but if humans are incapable of comprehending it, it is just another useless dead artifact. Practice, applied over a lifetime, is what creates the capability for comprehension. Asking an LLM to give you an answer creates an artifact. Humans being humans, most of their requests boil down to "make me rich without having to work for it," so the request itself is paradoxical and impossible to satisfy. Philosophers have only been saying this for all of human history, so don't hold your breath for any breakthroughs.
    • delis-thumbs-7e 6 minutes ago
      Precisely. I don’t really care whether LLM’s can produce code more and better than me. I learn languages, program and study computation to understand better the world we live in. Being a human being means increasingly being technologically augmented. To have any deep understanding of that world requires deep understanding of maths, physics, programming etc. that you can only gather by doing those things and solving problems with your meat brain.

      There’s a Twitch-streamer Tsoding who programs on C for fun calling it “recreational coding”. Maybe human programming will be a form of art in the future, virtually useless for big corporations to make money. I don’t care, I love it anyway.

    • charcircuit 3 minutes ago
      >The output of an LLM is useless without a human mind to comprehend it

      This is like saying software is useless if the user doesn't read the source code of it. This what happens >99.99999% a person uses software. People want to be entertained or have their problems solved.

    • gjskngnf 8 minutes ago
      > The output of an LLM is useless without a human mind to comprehend it.

      I don’t understand mRNA vaccines, but they are useful to me. The output of an LLM could at least in theory be the design to a major technological advancement, and its implementation with automatic tooling. We don’t have to understand that for it to be useful.

    • echelon 30 minutes ago
      > You don't study mathematics or computer science and information theory to produce commodities. You study them to transform your mind.

      That's nonsense. Of course you study them to meet demand.

  • siavosh 2 hours 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 1 hour ago
      Certainly humans can enjoy exploring such things, but will they really be needed?
      • dozerly 1 hour ago
        What does needed even mean? To produce shareholder value? Maybe not. To explore thoughts and ideas humans have for fun? Certainly
        • awepofiwaop 1 hour ago
          To make money in order to eat food and have a home.
          • siavosh 1 hour 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.
            • augment_me 52 minutes ago
              How do you think this will work? Do you think the whole of the rest of the world, about 7 billion people, will agree to give up on wanting to reach the western life standard that is currently consuming 4 Earth's of resources every year?

              Will all rich people in all countries collectively agree to be moved into tiny apts same size and give up their luxuries?

              If not, how do you define who gets what? Who gets to live in the fancy house, etc?

            • greesil 1 hour ago
              Right now that looks like a bunch of rich edgelords and us as serfs
            • breuleux 1 hour ago
              I don't think "abundance" is a stable state. There are always ways to use more resources and more energy, so no matter how much we have, it will never be "enough" -- abundance is just a transition state where a population or system has not yet figured out how to grind the surplus. The faster the progress, the shorter I would expect these periods to be.
          • delis-thumbs-7e 1 hour 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...

            • anon-3988 50 minutes ago
              If this is true, you would think that companies would be opening shops in the middle of (some shithole country) so they can make money (or someone else would grab it). But they don’t, why is that?
              • traes 40 minutes ago
                Because the shithole countries are poor and rife with violence that is hostile to operating a profitable company? Obviously?
              • delis-thumbs-7e 26 minutes ago
                Shithole country? You mean US: https://www.msfoodnet.org/about-us/hunger/

                The companies do not do this, because equal distribution of resources is poison to capitalism. The world where everyone are fed, and their basic needs - shelter, medication etc. - are taken care of, does not have trillionaires. Possibly not even billionaires.

                It is not profitable to give people humane standards of living. You work a lot harder when you see the homeless on the street on your way to work.

          • inopinatus 1 hour 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.
          • RealityVoid 1 hour 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.

    • willtemperley 55 minutes ago
      > The sheer surface area that AI can create in our intellectual life is limitless

      I agree with this statement, though I think this Brave New World is incredibly exciting to some and dystopian to others. The former group might include those that value the intellectual process above financial reward and status.

      The flip side is there are many people, especially in tech, where their area of expertise has evaporated along with their lucrative and previously high status careers. It used to be possible to have a technical job by essentially following recipes and it turns out AI is far better at that than a human.

      The linked article lays out why human understanding of mathematical models remains essential and I think the same applies to software. We're gonna need more software engineers who are able to think critically.

  • maniksaraf 17 minutes ago
    If we assume that trusting a model to execute an action is an ongoing exercise, since its trustworthiness is often discovered by the user organically as models develop, should trustworthiness be measured at the level of the model, or at the level of the human intent behind triggering it, whether explicitly or implicitly?
  • cjfd 53 minutes ago
    If we accept that AI is going to do all of these things humans will be superfluous and will just be optimized away. It looks a lot like we see the birth of silicon based life by the efforts of carbon based life. Carbon based life will die and it will not even be because AI decided to kill it, it will be because feeding and watering it was less important than other concerns. Bacteria may continue to exist, though.
  • imranq 1 hour ago
    The main reason to learn something is actually being able to communicate in the language of that subject. There are complex ideas in math that cannot be easily captured by the language of other fields. Pepole who don't study math cannot even understand what a worthwhile goal in math even is or how it could be useful to other fields.

    You can't simply prompt a model to be "better" when "better" isnt even properly defined

  • macrolocal 1 hour 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.

    • card_zero 35 minutes ago
      Ha, are you invoking something he said prior to discovering Russell's paradox? Which came about because he wanted to show that all of mathematics can be derived from logic about sets, but instead he showed that it couldn't be.
  • inopinatus 1 hour 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.

    • etrautmann 1 hour ago
      How is that relevant at all?
  • algorithm314 1 hour ago
    Life is all about tradeoffs. Mathematics have no tradeoffs. We need more engineers.
    • inopinatus 1 hour ago
      Life is all about purpose. Mathematicians are instead concerned with meaning. We need more philosophers.
  • calf 31 minutes ago
    I think this is the most beautiful letter on the subject I've read all year, it brought a tear to my eye. It's like reading those famous STEM letters/essays from history.
  • atleastoptimal 1 hour 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 1 hour 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?
      • itishappy 1 hour ago
        > AI doing math for math’s sake? And doing what with it?

        Stuff! Inscrutable stuff, maybe, but that's not "doing math for math's sake."

      • rudy6912 1 hour 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 1 hour 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 1 hour 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?

          • itishappy 47 minutes ago
            > 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?

            If you replace "LLM" with "mathematician" than this is the state of the world today. Stuff like Galois theory is beautiful mathematically, but what has it constructed or enabled for you and me?

        • altmanaltman 31 minutes ago
          There is a difference between manufacturing and design. Yes manufacturing is largely done by machines because of the nature involved but to look at a cpu and think 'no human was involved in creating this', you're wrong and also insulting to the humans who actually worked on things that led to the cpu and the manufacturing process.

          A cpu (the physical thing that sits in your mother) is not an abstraction, what are you talking about

    • dgacmu 1 hour ago
      We've been those ants for a million years, and only in the last 100 did we start to wrap our heads around quantum physics. We are the purpose behind creating LLMs. There's plenty in the universe we don't understand, and it's very human to keep striving to do so.

      If you believe that math is discovering, it's natural to think that all of that AI math already exists and is just waiting for us to find ways to discover and understand it.

      Don't write us out quite yet. :)

    • gaigalas 1 hour 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 1 hour 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 1 hour 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 1 hour 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.

  • bluejay2387 1 hour 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...