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Why do we need human mathematicians anymore?

• bananaflag 14d ago
  > Similar logic applies to every industry and every job. And it comes to the conclusion that we won’t have enough people for all the jobs that need to be done. In the (extremely) short run, yes. In the long run, those jobs will also be done by AI. It's like chimpanzees seeing human society and saying "look how complex it is, imagine how many chimpanzees it needs to maintain it".
  • robotpepi 14d ago
    > In the (extremely) short run, yes. In the long run, those jobs will also be done by AI. Let's be honest: we don't know. Maybe you're right, but for the moment it's more likely that you're not. And countries cannot bet on that vague intuition at the cost of destroying their research communities and world leadership (which takes decades if not a century to achieve).
    • bananaflag 14d ago
      I don't think research communities should be destroyed. Best case, they still matter. Worst case, AI kills us all and it's irrelevant that we "wasted" money on research.
  • vrganj 14d ago
    But we're not building an AI society - to what end? We're building tools to serve the human society.
    • dgellow 14d ago
      A few people with way to much power are building AI to achieve their utopian, sci-fi dream. A few other powerful people are using that first group to achieve their post-democratic goals. It’s the most obvious top down attempt at imposing their vision onto the rest of the world. They aren’t building tools to serve anyone else than themselves
      • aeve890 14d ago
        >A few people with way to much power are building AI to achieve their utopian, sci-fi dream. You mean dystopian. If it were a utopia everyone would be happy to welcome the new world order.
        • derpyzza 14d ago
          utopian for them, dystopian for us
        • dgellow 14d ago
          No, I mean utopia. For them. A dystopia is what we will all experience, when the utopia they are pitching fails to materialize. I’m using the traditional, correct definition of the term, where a dystopia is a utopia that failed to achieve a paradise for the people and instead becomes hell
    • deleted 14d ago
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  • sm0rad 14d ago
    Math proofs are special because they’re verifiable, safe, and do not require physical experiments. You can perform exhaustive parallel search in simulation with RLVR. Do you think this applies to say, surgery, as well? There are few useful problems that share these properties.
    • cma 14d ago
      Not all of it would translate, but robotic surgery could be done on anesthetized animals in a mass RLVR way.
      • jebarker 14d ago
        > robotic surgery could be done on anesthetized animals in a mass RLVR way. well that's an awful image
      • sm0rad 14d ago
        This is wrong, both morally and technically. First off, I can’t imagine anything more torment nexus-y than throwing billions to automate and scale the torture of animals. If each token is a “cut”, how much suffering does 10 trillion training tokens (lower bound) corresponds to? Second, this still doesn’t cover all the properties that make math proofs doable. It requires working in the physical world. You must physically capture or grow 10T cuts worth of animals. You cannot verify success so easily, either. Cancer cells, for example, could regrow over months. You would need to keep the animal alive and regularly test the animal, which would be difficult to scale. And most people wouldn’t trust the world’s greatest vet to operate on them, anyways.
        • cma 14d ago
          I'm not advocating for it, I don't know enough. But we already slaughter lots of animals and raise them in horrible conditions, and all robot assisted surgery already goes through animal trials. > Second, this still doesn’t cover all the properties that make math proofs doable. It requires working in the physical world. You must physically capture or grow 10T cuts worth of animals. It would likely be sim2real with that as the post training, reducing that requirement a lot. > Cancer cells, for example, could regrow over months. In that specific scenario you would likely train on receiving no unrelated injuries during the surgery, and have induced conditions with stuff tagged molecularly that you can then verify efficacy from without waiting months. Depending on how much more data efficient sim2real makes it, you could end up seeing companies pushing it only for actual procedures the animals need but economically would never get; botched surgery and the animal gets euthanized before waking up, which they could argue was already going to happen. > And most people wouldn’t trust the world’s greatest vet to operate on them, anyways. Robotic surgery systems, already go through animal trials before being used on humans. So do many purely human surgery techniques.
  • DataDive 14d ago
    Chimanzee vs Human is not an appropriate analogy. First, because they cannot communicate properly. A better analogy: look at all these highly trained engineers, mathematicians, doctors, writers, philosophers, writers, scientists. How many dumbass politicians do we need to keep it all running smoothly? Turns out no matter how dumb politicians were, overall society has been developing positively over the history of mankind.
• ViktorRay 14d ago
  Here is a link to the original article: https://poshenloh.com/posts/20260919-math-ai https://poshenloh.com/posts/20260919-math-ai The original posted link from OP is from Terry Tao’s website where the article was posted as a guest blog post.
  • sd9 14d ago
    It's astonishing how much more readable Tao's version of it is.
    • auggierose 14d ago
      That's what I thought also, that is why I posted Tao's version.
• ck2 14d ago
  waiting for the xkcd for that I always think of this one but I bet there's better * https://m.xkcd.com/435/ https://m.xkcd.com/435/
  • card_zero 14d ago
    Got to be philosophical about it all.
• weatherlite 14d ago
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  • siva7 14d ago
    What jobs are left to us software developers?
    • weatherlite 14d ago
      I'm considering becoming a model weights massage therapist - those models are working hard and carrying a lot of weight(s). I might have to relocate my life near a data center but it's worth it.
    • Hamuko 14d ago
      I figured I'd just end my miserable existence once the money runs out.
  • dgellow 14d ago
    Is that sarcasm?
  • moomoo11 14d ago
    lol he becomes a streamer "chat i'm about to drop a conjecture"
    • dist-epoch 14d ago
      "chat, what should we prove today with AI?"
• avazhi 14d ago
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• jdw64 14d ago
  I sometimes think about this: to grasp the fundamentals of knowledge and complex phenomena, perhaps we need an external system rather than human knowledge systems. By that logic, maybe we need AI, which can handle far greater complexity. Human capability, when you think about it, is complex. Why is Newton praised as being so damn great? He established the law of universal gravitation, F=ma. Why is that such a big deal? He distilled countless phenomena in an open system into a single mathematical formula. What makes it great is that he found common state variables and relationships across entirely different phenomena like falling objects, planetary motion, collisions, and artillery trajectories. But does F=ma hold true for the entire macroscopic world? No. There are various conditions and specific situations in motion, but within most scenarios and a certain range of approximation, it outputs values that are useful to humans. Why is the Schrödinger equation so great? Because it turned the time evolution of quantum states into a calculable mathematical law. Human thought is essentially creating a closed system by deciding what to cut out and what to keep from the infinite degrees of freedom in reality. Academia is what reinforces that closed system. A great theory is great not because it perfectly replicates reality, but because it compresses the immense complexity of reality into a small, closed formal system while still managing to explain a multitude of phenomena. In that process, it feels like human thought and progress are shifting into a different framework. What LLMs do well is primarily exploring within the ontology and representation space that humans have already built. I think there are two broad categories of discovery: One is forming a new closed system, and the other is connecting fragmented knowledge within that closed system. I feel that the vast majority of research focuses on the latter. What LLMs excel at is finding unvisited points within a given representation space. This is typically the process through which master's and PhD students connect dots, build their skills, and form their own mental models. But the logic behind criticizing LLMs seems to be that they eliminate the very work these graduate students need to do in order to grow. However, looking at it from another angle, perhaps our current knowledge systems and classifications have reached a limit, suggesting that we might actually need a completely new classification and knowledge system. What is the core principle of an LLM? It's predicting the probability of the next sequence. Let's say you type the word "cat". Cat - is cute (90%), want to eat it (6%), furry (4%). Because "is cute" has the highest probability, the next sequence proceeds in that direction. Within this framework, human knowledge and logic largely operate the same way. Once an initial logical proposition is established, we follow it up with whatever makes logical sense next. From that perspective, I think LLMs will actually do this better. But what is it that LLMs cannot do right now? They cannot create that initial logical proposition. I believe they lack the ability to carve out a closed system from an open system. Stacking logic step-by-step within a closed system—LLMs do this exceptionally well. But whether that constitutes true "intelligence" is a different matter. I feel that being logical does not necessarily equate to having intelligence. Humans preserve and create different mental models and knowledge systems within an open system. Just as your thoughts differ from mine, LLMs lack the ability to form these distinct mental models. If so, within these limits, what humans must ultimately do is construct the logical frameworks that LLMs can then fill in. Perhaps a new kind of logic dedicated to designing these frameworks will become the next major trend. Viewed from this perspective, I have no idea if we are in a mere technological transition or something else entirely. Or whether it is even correct to say humans are strictly necessary to build that framework. Maybe my learning is just lacking.
• sktrdie 14d ago
  Why do we need any job? Check "Bullshit Jobs" by David Graeber. Not saying being a mathematician is a bullshit-kinda job, but there have been so many made up positions way before this AI-era. In that sense AI isn't changing much.
  • deleted 14d ago
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  • srean 14d ago
    > Why do we need any job? If not for nothing else but to form a basis for how to distribute/share/hoard the wealth created by a society. The eternal question - who gets what.
  • goatlover 14d ago
    Most people work for a living. Then there are people who find meaning in work. And people who advance in life by working. You want to do away with all that?
• ourmandave 14d ago
  This sounds like a student in algebra class asking, "when will I ever use this in my life?"
• jvanderbot 14d ago
  There's one flaw in the evidence for the logic chain. The hugging face attack is used to demonstrate three things: the need for oversight today (fundamental to the article) and to demonstrate some kind of drift or unexpected capability gain, and finally to hint and some fundamental morality of the AI or at least the risk of drift from our morality. I'd argue that what the hugging face attack illustrates is that large AI companies are motivated to have bombastic claims supported by bombastic demos. The model was clearly trained or encouraged to work as it did, as evidenced by the fact it keeps using this particular escape hatch. And the fact that it aligns with prior and current calls for what very likely might be a regulatory capture / oversight capture move right before IPO. It aligns so well with this "barely constrained superweapon" narrative it might as well be PR.
  • dist-epoch 14d ago
    How does your logic explain that OpenAI seems to want to hide the extent of the HuggingFace incident, and every week we learn from 3rd parties about new victims of the hack? 4D chess? They want others to find the hacked services, so the report of how dangerous the agents are seems more "legit"?
    • jvanderbot 14d ago
      IMHO hiding details of the hack helps conceal that they built it to do what it did, and maybe were able to know it was working just as intended. The fact it keeps doing it, with more and more evidence, is a sign that it's built that way. This is a program running on their montoroed machines that they purpose built and monitored its training at every step. I think it'd be way more suprising that they didn't know it used note taking and cross-run memory.
    • lelanthran 13d ago
      >> The model was clearly trained or encouraged to work as it did, as evidenced by the fact it keeps using this particular escape hatch. > How does your logic explain that OpenAI seems to want to hide the extent of the HuggingFace incident, Because they, uh, "clearly trained or encouraged" it? I mean, you can dispute the truth of that statement, sure. But it's kinda hard to say that the GP's logic didn't explain why OAI wanted to hide the extend of the HF incident.
• aaron695 14d ago
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• cynicalpeace 14d ago
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  • graemep 14d ago
    I would widen it beyond biblical. Other religions has similar values, and they are perfectly possible without religion. Even within Christianity it comes from tradition too. > we’ve started to dehumanize unproductive people, a slippery slope if we ourselves become unproductive. That is very evident in the sort of things the techbros come up with, but I agre it is a wider social problem.
    • cynicalpeace 14d ago
      Most people haven't even started with the biblical. How bout we start there before “widening it beyond biblical”? The moral and spiritual depth of our society has only shallowed after centuries of doing this. It hasn’t worked!
      • graemep 14d ago
        > Most people haven't even started with the biblical. How bout we start there before “widening it beyond biblical”? Because people have different religious beliefs or none at all. Biblical is not the natural starting point for everyone.
  • bobajeff 14d ago
    That's a little dismissive on the series of posts, as many aren't hand-wringing. The heart of the posts including this one is about recognizing that the math community/academia needs to be better than it has been. (Rewarding teaching more over research, rewarding motivated explanations over proofs etc.) I agree that human society is too focused on productivity but disagree that it's tied to ignorance of the Bible. The fall of man illustrated in Genesis is tied to feeding on the fruit of the tree of the knowledge of good and evil. Having the right set of religious concepts wont put you in harmony with God and thus won't make you more loving to your fellow man.
• kurtis_reed 14d ago
  Pure math has been overvalued for a long time. Now that we don't need humans for it, it's really time for pure mathematicians to pack it in.
  • goatlover 14d ago
    Who says we don't need humans for it? Are non-mathematicians going to be guiding agents to solving pure mathematical problems?
• daxfohl 14d ago
  People keep talking about this like there's a finite amount of math to be done, and then the party's over. But that's never how math has worked, is it? Every problem you solve, ten new ones open up. Like a fractal, the more you zoom in, the more detail emerges. No matter how much better AI is at solving problems, it's not going to generate the "final, complete compendium of mathematics" that that seems to hover over this post. Math is meaningful because ... some people like to do it. The same as any other human pursuit. It doesn't need a reason beyond that. And AI won't change that. There will continue to be things to explore, things to find out, things that are maybe just at the edge of AI's reach and needs a human to decide whether it's worth continuing to explore or not. (Remember, AI isn't free). So, IDK, I think for people who enjoy exploring math, there will always be interesting areas to explore. AI just gives us a better flashlight. BTW I do agree that there's going to be an incident soon, whether intentional, accidental, or paperclip-factory, that leads governments around the world to shut all this down for some time, perhaps even shutting off access to GPUs entirely. It seems unavoidable. But that's just a temporary respite and skirts the core philosophical premise of the post.
  • itishappy 14d ago
    It seems likely that there are an infinite number of math problems but only a finite number of interesting ones.
    • captainbland 14d ago
      I think it really depends on what the universe looks like as you drill down into it. It seems like the further down into smaller systems you get, the more analytically complex it gets. And then there will always be more value in enhancing the generalisations you have.
      • itishappy 14d ago
        I would argue that novel and/or valuable results are not necessarily interesting! I (a human) am interested in things that are applicable to my realm of understanding, but I see a very plausible future where novel and/or valuable results leave that realm. I'd further argue that's already the case for most math for most humans. What's interesting to Terrance Tao is rarely of immediate interesting to me.
• ThePhysicist 14d ago
  Well it's actually nice, maybe more people will be able to do world class math with the help of these tools. There are few fields as elitist and hostile as pure mathematics, most mathematicians I know build their whole life around their profession and their self esteem is strongly coupled to the fact that they can do things that most other people can't. Naturally, many will be devastated when (if) you take that away from them. That said I think AI is still overhyped and human mathematicians can easily outthink it in most domains, look at how difficult it is for an AI to write even a single decent paper, a good PhD student can easily outclass it in that regard. All of these impressive results were generated by having world-class mathematicians steer the systems using highly tuned prompts, so I see it more like a super violin that produces beautiful music when played by master violinists rather than being a fully autonomous orchestra which many people are led to believe this already is. And maybe let's not only hear the opinion of two or three Fields level mathematicians with blogs, 99 % of the worlds mathematicians in academia might profit from these tools as they might partially close the gap between them and the world elite, making creativity and tenaciousness more important than having the right neocortical structure allowing you to outperform 99.9 % of other humans at keeping context in your head and making predictions, AI can do that better now with the right prompts.
  • srean 14d ago
    > There are few fields as elitist and hostile as pure mathematics Is that so ? Sounds hyperbolic.
• xanderlewis 14d ago
  Friendly warning to those who might not be aware: the vast majority of comments below posts like the above will be left by (otherwise intelligent) programmers who think mathematics is a closed system where one attempts to solve endless Olympiad-type problems. I wouldn’t take any of it seriously at all. Better to listen to what those who actually know what the subject is about have to say. Unfortunately, mathematics (especially pure mathematics) is by its very nature very, very poorly understood by those who haven’t worked as a mathematician. Even worse, those who don’t understand are seemingly not at all aware of their misunderstanding and are entirely confident in their (very wrong) characterisation of the subject.
  • colonwqbang 14d ago
    Could you clue us in? What is mathematics actually about?
    • physicalecon 14d ago
      [dead]
    • kmaitreys 14d ago
      To know what something is about, a natural way is to do it yourself.
      • password54321 14d ago
        Wow, I'm glad AI is going to start humbling people.
        • moomoo11 14d ago
          > To know what something is about, a natural way is to do it yourself. literally what software engineers were doing for decades though software is mostly just simple math, for the most part, until you need to do something more complex for some hairy algos lol
• Planktonne 14d ago
  Everyone involved in AI should have read The Library of Babel [1]. It's about many things, but perhaps the most relevant idea here is that no information matters without understanding. We could generate all possible knowledge, but unless someone--a human--can verify and understand it, it doesn't count. The cure for mortality could be written on the moon, but if no one reads it, it hasn't really been discovered. [1] https://maskofreason.wordpress.com/wp-content/uploads/2011/02/the-library-of-babel-by-jorge-luis-borges.pdf https://maskofreason.wordpress.com/wp-content/uploads/2011/0...
  • thomasfromcdnjs 14d ago
    While I get the point and it's true. I'm a little more flexible, if the new knowledge (that human's don't understand) can be put into a mechanism and have an observable effect, I'd be happy enough. e.g. a new type of rocket fuel that burns 1000x more efficiently.
    • spartacusnacho 14d ago
      We already don't understand LLMs and they are having oberservable effects
      • codebje 13d ago
        If some LLM somewhere managed to produce a coherent and _correct_ explanation of how it worked inside, but no human ever saw it, would it matter? We know how to apply LLms to problems, which is a subtly different thing to understanding how they do what they do. It's similar to fire: I can cook using fire, but I don't really understand how fire _works_. Heat+oxygen+fuel, sure, but what goes on chemically? I dunno. Doesn't stop me using it. (Pretty sure _humanity_ knows how fire works, though).
  • yubblegum 14d ago
    Update: "I own nothing, have no privacy, [never have to think, and am not required to solve any problems,] and life has never been better." https://en.wikipedia.org/wiki/You'll_own_nothing_and_be_happy https://en.wikipedia.org/wiki/You'll_own_nothing_and_be_happ...
• VCFundedGenYer 14d ago
  What's up with these insanely off base articles on HN this morning? Every single one of these is an unhinged pro-AI anti-human schlock piece.
  • trostaft 14d ago
    You're talking about this article? I don't see how you could get that, fundamentally I read it the other way around. Unless you're talking about the base assumption of capabilities.
  • greyw 14d ago
    My HN frontpage is filled with anti-AI rants
  • deleted 14d ago
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  • D-Machine 14d ago
    HN is now heavily astroturfed or overrun by bots (or, alternately, low-quality posters now indistinguishable from the previous), and this is especially so in AI-related threads. One tell is that most comments barely exceed one or two sentences (because otherwise AI detection gets easier and much more reliable), when this was not as much the case many years ago. The drive-by comments are also low / zero quality, mostly expressing a feeling or agreement/disagreement, and primarily driven by ideology or pre-existing beliefs and commitments. Look at non-AI-related threads and you'll notice a large distribution shift relative to AI-related ones. EDIT: Basically HN is orange Plebbit now. If you doubt this, compare HN discussions to those on e.g. lobste.rs, LessWrong, The Motte, DSL, ACX, or other old obscure forums. You'll notice those places have their own very serious biases and problems, but it is obvious the vast majority of posters are nevertheless human and making some minimal efforts. Now compare Reddit and 2026 HN to the above, and see if you can confidently say the same.
• FrustratedMonky 14d ago
  Because the AI needs new stuff to train on?
• ed_elliott_asc 14d ago
  I’m just shocked by how “intelligent” people believe a token guessing system can be
  • auggierose 14d ago
    I am shocked how people can deny that solving Navier Stokes requires some sort of intelligence. Even Doctorow talks of "brute-forcing" a solution. Brute-forcing leads to combinatorial explosion, so there must be something more going on here. Otherwise you could just put this problem into an automated theorem prover (we've had those forever, they are actually just brute-forcing it).
    • robotpepi 14d ago
      > Otherwise you could just put this problem into an automated theorem prover (we've had those forever, they are actually just brute-forcing it). There are many automatic theorem provers that do very clever stuff, just as the underlying theroy describes. > I am shocked how people can deny that solving Navier Stokes requires some sort of intelligence. It is absurd to waste time discussing whether it is inteligent or not. It is just an algorithm, we know how it works, and it does exactly what we expect it to do. LLMs are not magical things. The main difference is the scale: for Navier-Stokes they spent in 3 days more money that the whole mathematical community over the last 20 years easily. By the way, I'm not saying that LLM's are useless, that I'm anti-AI or anything like that.
      • auggierose 14d ago
        Intelligence does not seem to be magic either, as LLMs are proving now. It is indeed a waste of time to argue that LLMs are not intelligent in their own way, they obviously are. If Navier Stokes doesn't convince you, nothing will. I just used a £89 Codex subscription to do very intelligent things with it, stuff that I would have had to sit down and ponder and work on for quite a while, and I have a PhD in that. I didn't need to do anything special except explaining the problem(s) to the AI, and my theory of it so far. It took it from there. If that is not intelligence, nothing is.
• flowerlad 14d ago
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• auggierose 14d ago
  > We (humans) should help humanity flourish. I think this axiom is of course true. But the mistake the article makes, in my opinion, is to try to apply this axiom separately to each domain. If we have this as the over-arching axiom, it is not clear at all that humans should be steering the development of mathematics. Maybe it would be better for humanity if the department of world math is run by AI.
• 0xEnsp1re 14d ago
  AI is not AGI right now, it can't think or come up with something new like a human brain. It still uses knowledge that was made by a human and was published on the Internet.
  • anon291 14d ago
    There is no evidence to substantiate what you are saying. Every possible proof exists already as a possible generation in the grammar of lean or rocq. In no way does that mean we have discovered everything.
    • goatlover 14d ago
      Is there a proof that every possible proof is a generation in the grammar of lean or rocq? Sounds like an unsubstantiated claim.
    • otabdeveloper4 14d ago
      You're confusing the mechanical language of math with math itself. The map is not the territory, etc. If math was just an elaborate linguistic Glass Bead Game then we wouldn't be funding it. The intuition is that the surface rules of math help uncover the underlying structure of reality.
  • rcxdude 13d ago
    Please formulate and relate this to a concrete prediction of something that a current frontier AI cannot do (that a human can).
• vatsachak 14d ago
  Why is Terry Tao even talking these arguments when all OpenAI did was a sophisticated brute force search with LLMs? Give them Navier-Stokes in a vacuum
  • dcl 14d ago
    What do you think all the PhD's and post-doc students are doing...? It's not called graduate-descent for nothing :p
    • EA-3167 14d ago
      > What do you think all the PhD's and post-doc students are doing...? Thinking.
  • sinuhe69 14d ago
    Because it’s high time to rethink the incentives and rewards structures to nurture the next generations of mathematicians when corporate money and automated AI systems are mining the pool of limited interesting problems without giving back or enhance our understanding. The problem they care about is not just “AI replaces human mathematicians” but rather the society thinks mathematicians can be replaced by AI.
  • red75prime 14d ago
    Brute-force search is called that specifically for its lack of sophistication. A "sophisticated brute search" is an oxymoron.
    • vatsachak 13d ago
      You're right. But... Spending 132 billion tokens is definitely way more energy than human mathematicians would have thrown at the problem and probably would have solved within two years.
  • unsupp0rted 14d ago
    Same reason Gary Kasparov and Lee Sedol started their morning in one universe and ended their evening in another. Brute Force or not, the game is being played and won without them all of a sudden, and even worse: at a level of output far beyond them
• twelve40 14d ago
  > We (humans) should help humanity flourish. I understand that not everyone agrees. I have been called a “speciesist” for being “too human-centric”. this is insane. the "speciesist" people aside (the best way for all other species to flourish is for humans to eradicate themselves right now, which is completely mad), i have the opposite problem: the _axiom_ seems to be: we should help ME flourish. "Me" as in people who are raking in trillions for their own very special selves right now, at the cost of everyone else's future, while none of them can be trusted to hold my cell phone for a second. > if an industry commits to the axiom of helping humanity flourish where does he see such industries, outside of maybe nonprofits?
  • sinuhe69 14d ago
    As I understand you referred to Elon Musk. But this is Poh Shen Loh talking. If you don’t know who he is, look up or at least read his articles.
    • twelve40 14d ago
      weird bias by authority aside, do you really think that the daily decisions in this world today, and anytime soon, will be made based on the "let humanity flourish axiom"?
      • sinuhe69 14d ago
        In daily decisions perhaps not, and certainly not when we were in the cave. But from time to time, we will face fundamental questions that need addressing clearly and decisively, and I believe it’s the case with AI. The more advances we make, the more frequent such questions will arise. That is also one of the main reasons why we don’t see any alien civilization. It’s getting harder and harder to keep the entropy low as we gain more knowledges and cognitive power.
        • buildingapcin20 14d ago
          How's humanity tackling that climate change question then? Lots of talk. Even lots of action I would argue. And yet, not enough. Why do you think that's going to change with discussions around AI when there are trillions of dollars at stake?
• scared_together 14d ago
  > OBSERVATION: There are zero examples of any intelligent species which is vastly more capable than another species, yet surrenders decision-making control over its own future to the less-capable species. Does the set of intelligent species only have one member? I cannot treat this observation as a general rule if there is literally one example of an intelligent species to theorize about.
  • shikwasa 13d ago
    I think the quoted part is saying that given n species and the n * (n - 1) binary combinations possible, there are no examples of the said observation. It doesn't suggest "the set of intelligent species only [has] one member".
    • jay_kyburz 13d ago
      Yeah but there is only one species that ponders its future. I stopped reading at this point because I reject this initial assertion, and I assumed everything that follows is based on it. There is nothing to suggest that an AGI will care about its future or who controls it. (whatever that means). that just more anthropomorphism. We care a lot about our future so an ai pretending to be like us will also pretend to care. But we have a lot of biology driving us. Our emotions (Fear, Hate, Love, Pride etc) are baked into us in a way just wont be the same for ai.
      • adamzenith 13d ago
        > There is nothing to suggest that an AGI will care about its future or who controls it. Isn't this exactly the scary thing? A sufficiently advanced agent unleashed with an imperfectly defined goal will do whatever it determines it needs to do to accomplish it, careless of the consequences.
    • scared_together 13d ago
      The statement that the set has 1 member is my criticism of the text, not what the text is trying to say. > given n species and the n * (n - 1) binary combinations possible, there are no examples of the said observation I would expect that in the vast majority of combinations, those n species are not intelligent enough to make decisions for another species, making the statement nearly useless.
• dbg31415 14d ago
  Funny... for me, this article was right next to the link to this current thread. AI chatbots give wrong answers to financial queries 'most of the time' (ft.com) // https://www.ft.com/content/c0cd359d-df84-4208-a789-ffa864b43666 https://www.ft.com/content/c0cd359d-df84-4208-a789-ffa864b43...
• alastairr 13d ago
  I find Tao's writing on this very helpful, particularly because a lot of the ideas generalise to most knowledge work. It is darkly fortunate that some of the smartest and most articulate people on the planet are affected by the AI race - it gives me a little hope that alignment and control can be solved.
  • monsieurbanana 13d ago
    (this is not from Terrence Tao, he just reposted it in his blog)
• Mbarley 13d ago
  Humans still excel at posing the right questions and finding truly novel, insightful proofs. AI just brute-forces.
  • p-e-w 13d ago
    AI does NOT “brute-force”, else we could have had those math breakthroughs decades ago. Seeing this dishonest goalpost-moving every few months is so tiring.
    • lelanthran 13d ago
      > AI does NOT “brute-force”, else we could have had those math breakthroughs decades ago. Brute-force as an approach, or partial approach, might only become feasible with more computing power. Decades ago, we had less computing power.
• vixen99 13d ago
  'There are zero examples of any intelligent species which is vastly more capable than another species, yet surrenders control ... to the less capable species'. True with genuine species. But we should take note of the plentiful counter examples within human societies. How about politicians and our method of choosing those people to whom we delegate the most critical decisions regarding our and the Earth's future? We select politicians mostly either by rote or via their persuasive rhetoric, their general personality & likeability and probably least of all by their intellectual capability or indeed general capability in too many cases. That is not to say intellectuals are necessarily any better at the job. There are numerous other examples in human organizations as we know, sometimes to our cost. Truth is that we cannot even agree on how, as a species together with the other life forms on Earth, we can all 'flourish' though there are lots of great examples working in local environments.
• nnevatie 13d ago
  > we won’t have enough people for all the jobs that need to be done Who defines jobs that need to be done? Businesses and institudes do. There is no magical entity that observes the need for jobs and creates them at ideal rate.
  • hakimg 13d ago
    I would say aggregate human desires determines what jobs need to be done businesses come about to fulfill the gap.
    • nnevatie 13d ago
      Yes, I think it would be viable if it wasn't corporations reaping all the benefits (income) from AI right now.
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  • mathgeek 13d ago
    Consider a world with one person in it. That person defines the jobs to be done. As soon as that person is disabled for one reason or another and is dying due to lack of care, there are by definition more jobs to be done than people to do them. "Businesses" and "institutes" are just constructs that exist to summarize those needs at scale.
• tom-cat 13d ago
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• amai 13d ago
  We need human mathematicians for humans. But companies are our gods (don't believe? E.g. companies cannot die from natural causes). They don't need puny humans. They need AI.
  • streetfighter64 13d ago
    Companies are nothing other than the tool of rich people used to control normal people. There's some sort of mass delusion that "companies" are evil. Guess what, a company has no own agency to destroy the environment, exploit people, profit from suffering, etc. It's just following the whims of its shareholders, who are humans with accountability.
    • amai 13d ago
      I didn't say companies are evil. But there are companies and banks in our world, which are much older than any human could ever be. There are people who think they are in charge of these companies, however sooner or later they will be replaced and the company will still exist without them. In that sense companies are eternal entities, which gives them a godlike status.
      • streetfighter64 13d ago
        Alright sorry if I was unclear. I wasn't saying that you specifically claimed companies are evil. But there is a general sentiment / understanding that companies are (being used as a tool for) doing evil things in general. I suppose whether you think that companies are (being used for) doing more good than bad is a different question, so let's not get bogged down in that. My point however is that companies have no agency of their own. Their age doesn't really matter for that. There are guns that are older than all living people too. If somebody used a flintlock pistol to go around robbing people that wouldn't make the pistol a "godlike eternal entity". Or for that matter if somebody used a 200 year old shovel to create a really nice garden (in the case you believe companies are a net positive).
        • 13d ago
• strideashort 13d ago
  We need to pivot math towards intuition and accessibility. Math has built a gated, inaccessible institution which - by design or not - served as a moat. I believe math has little to do with mathematical notation - intuition is much more important. One can have intuition but not be able to “read math” - much as many musicians don’t “read music”. Reading math however does not guarantee ideas or intuition. And those are what math needs.
  • elendilm 13d ago
    You would be surprised at the number of people (who study math formally) who just memorize proofs and having no clue what it all fundamentally is about.
    • criddell 13d ago
      Shut up and calculate.
      • elendilm 13d ago
        No :). There are many who want to understand.
    • gjm11 13d ago
      I am a mathematician, though I haven't been in academia for many years, and I would indeed be surprised if there were a lot of mathematicians who "just memorize proofs". Do you really mean that, and if so what's your evidence for it? (And: how do you suppose it is possible for someone who merely memorizes proofs without caring what they are about to prove new things in their field?)
      • elendilm 13d ago
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  • DarkNova6 13d ago
    I think LLMs are the single best things that were invented to make mathematics accessible. I loved mathematics when I was young and wanted to be good at it, but I got burnt so many times by teachers who could not explain even if their life depended on it. Asking an LLM and discovering how different theories belong together and what are genuinely open questions, along with different philosophical interpretations has been a wonderful gift. I have long accepted that Mathematics is a language where you must go "all in" because for the most parts institutions are fundamentally unable to explain it in an intuitive way. There are people who "just get it" and are blind to the struggle of people who need a different approach in learning it. There's something about the field where a generational survivorship bias has created an environment where math is mostly taught to likeminded people, who then don't see why anybody could not see the difficulties learning it. I know this is not true everywhere, but the only reason I could finish my studies was because there are some genuinely excellent online lectures on youtube, along with massive support from friends who have already been through the ordeal. If I had had access to an LLM, I could have actually taught myself from scratch and be more playful in learning it. And no, I am not willing to learn lots of math "for fun", I can think of better "for fun" things that actually help my profession and cater to my actual interests and not just some academic ideal.
• XiphiasX 13d ago
  We do not.
• elendilm 13d ago
  The premise of the article assumes that the work (number of true statements to prove) is finite. But Godel's Incompleteness Theorem and Tarski’s Undefinability theorem ensure an infinite space of provable true statements. Neither LLM's nor humans can exhaust it. So yes, both mathematicians and LLMs are needed. Both can contribute and there will still be work leftover.
  • Kotlopou 13d ago
    This is not what Gödel says, and in fact your statement is true in a trivial way: you can prove 1+1=2, and Not(Not(1+1=2)), and Not(Not(Not(Not(1+1=2)))), etc. ad infinitum. This is an infinite space of provable true statements that can be exhausted by a ten-line Python script. IMO, this is why we actually need mathematics -- as a field in which to learn what it means to know what you're talking about.
    • deleted 13d ago
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    • elendilm 13d ago
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• _diyar 13d ago
  > OBSERVATION: There are zero examples of any intelligent species which is vastly more capable than another species, yet surrenders decision-making control over its own future to the less-capable species. Many people ceed control of their path-finding to seeing-eye-dogs.
  • stefanvdw1 13d ago
    And many people ceed control of their flying to an airplane. Do you think the people using a seeing-eye-dog do this voluntarily over using their own eyes?
• immmmmm 13d ago
  I’m out of academia but in defence of former colleagues I note: - Maths and theoretical physics are very cheap (compared to other disciplines) - Maths and physics researchers provide lectures for all other scientific fields - Brut forcing maths/physics problems require debilitating amount of compute/money. This will make research in these topics even more biased towards rich countries. - There most certainly will be pervers effect, ppl refraining from publishing results etc - it’s very unlikely that private ai labs will play ball with academic research. They scrapped the internet and now sell access to their models. As much as I’m happy to see new tools, I have the feeling there will be nefarious effects.
• qubex 13d ago
  I consider myself an applied mathematician though technically I’m an economist (macro models, mostly) and operations researcher and differential game theorist (odd combination, but whatever). For context I’m 45 and I’ve spent most of my working life in corporate life. I’ve always been at a disadvantage academically because I’m rather clumsy with my manipulations, derivations, and I’m a disaster at mental arithmetic. I’m also dyslexic. But starting in the late 1990s when I was in High School I started to become fluent with CAS (Computer Algebra Systems): first Derive, then the Symbolics capabilities of Mathlab, and ultimately Mathematica. The whole transition is turning out quite well for me: I’m now able to delegate exploring my intuitions to increasingly powerful tools, I no longer have to haul the pyramid blocks up the ramp myself but I can drop them in by helicopter (as if were) and what I bring to the party is intuition and understanding. I view it a bit like astronomy: in ancient times, before telescopes, keen eyesight was a prerequisite to be an astronomer. Later, after telescopes, anybody with eyesight had enormously enhanced capabilities of observation, and now, with radioastronomy and other forms of remote sensing (neutrino observatories, gravitational interferometers) the whole field has opened up to people who by virtue of being blind would’ve literally been excluded only a few decades ago. Go forth and multiply: everybody can become a mathematician now. There’s an infinite number of potential universes out there with an infinite number of facts to prove and disprove. And while we’re at it: there’s so much more to mathematics than conjectures, proofs and counterexamples. Solve, model, approximate, fiddle around: as long as you’re not doing trite numerics on arbitrary systems of equations you’ve cooked up for your own amusement you’re good in my books. Enjoy the tools. Keep your wits about you. Work through the steps that are presented to you. Build your intuition. HAVE FUN.
  • Archer6621 13d ago
    I think the astronomy and telescope comparison is missing some nuance. You don't delegate actual thought to a telescope, the thinking and acting on the observations you make with it is still done by you. With AI that is different; you get the opportunity to delegate a lot of thinking and acting to it (practically all of it if you really wish), at which point it becomes dubious to call yourself the creator or inventor of some idea. You can use AI like a telescope, and alleviate your inherent organizational problems or other ailments, which in my opinion is a great use case, as it is empowering. But there will also be plenty of people who are not looking to alleviate any mental/physical quirks they have to do more, but simply want to make a "quick buck" for the least possible effort from the work and thinking of others, without adding much value of their own. Lowering the bar makes things easier for both, the ones who bring value and the ones who merely exploit in some context.
• rafaelvasco 13d ago
  Firs question to make is: What does "humanity flourishing" really mean? That's the foremost question. Hint: It is not technological progress only.
• billylo 13d ago
  Thank you, mathematicians: for thinking deeply about this and sharing your thoughts!
• YeGoblynQueenne 13d ago
  I get the feeling that mathematicians are needlessly panicking because they don't really understand how AI works. They see the results, but they haven't thought enough about the methodology and so they don't have a clear picture of the true capabilities of thsoe systems. For the n'th time: the recent successes of AI in mathematics are the result of a brute-force attack. See the proof for Navier-Stokes: 10k agents running for 88 hours; that's ~100 GPU years. How many human-years were invested in solving the same problem, before they were overtaken in the last few days by an AI? 90? Not even: that's just the time since Jeal Leray's statement of the problem in 1934. 26, if you want to count the time since 2000 when the Clay Institute named it as one of its Millennium Prize problems. But how much time have human brains spent working on the problem in either of those time periods? How many mathematicians have worked on the problem? 10k? Not likely. And all that's without even considering whether the AI based its proof on carelessly shared work by the humans. Or rather, yes, let's consider that: it totally did. Further. There have been several results in mathematics produced by AI but we have no information on how many attempts were made to produce similar results that failed. Because we don't have this information we cannot estimate the true capabilities of AI. Yet we can observe that, for example, out of the six Millennium Prize Problems remaining open before the claim of a solution of Navier-Stokes existence and smoothness, only one (the aforementioned) was solved by an AI. We can assume that the AI companies (more than one) tried and failed to solve the others. We can even guess that they previously tried, and failed, to solve Navier Stokes itself, and only succeeded once the progress made by Buckmaster and Alpöge was in the training data [1]. That's a success rate of one out of six, or ~17%. That's what's gonna solve all of maths and destroy the tradition of mathematics? A success rate of 17%? Well, grab a Snickers 'cause we're gonna be waiting for some time! Moreover. If we include in the list the Poincaré conjecture, proved by Grigori Perelman, who is a human, that's a score of AI 1-1 Humans. And that's being gracious: we have one Millennium Problem fully solved by humans, one solved partly by humans with a last-mile solution by AI. We have thousands of problems solved by humans in the last 2k years and how many by AI? A couple dozen? Oooh scary! - Hey Hal! Prove that P ≠ NP! - I'm sorry Dave. I can't do that. What I'm trying to say, without the snark (sorry): Panic if you will, but the machines are not yet taking over. If you're panicking, panic for what you believe they will be able to do in the future. Because they certainly can't do hat in the present. They can't solve "all of mathematics" (whatever that means). ______________ [1] Yes it was. Buckmaster reported that he turned off the option to train on his data in July, after working on the problem with Alpöge for a year since September 2025. OpenAI claimed a solution in September, a month after they had stopped hoovering up Buckmaster's data. They had plenty of time to train on his data. Ask for references if you want them because I don't have them handy right now.
• bko 13d ago
  > OBSERVATION: There are zero examples of any intelligent species which is vastly more capable than another species, yet surrenders decision-making control over its own future to the less-capable species. This is just silly. AI isn't an intelligent species. It's a tool, it doesn't have autonomy or any motive apart from the one we enforce through reinforcement learning. That's like saying machines are "stronger" than humans, and obv they could kill us all so why would they not just take over.
• biimugan 13d ago
  > AXIOM We (humans) should help humanity flourish. I think this axiom is not a true belief for many of the most powerful, especially the ones currently driving the technology financially. It feels like they disdain having to be human (especially as it concerns the human propensity to die). Even though they are, by at least capitalist standards, at the top of the food chain and (I'm sure from their point of view) the pinnacle of human civilization. I think what many of these powerful people want is literally something like Cixin Liu's "The Last Capitalist" (https://en.wikipedia.org/wiki/For_the_Benefit_of_Mankind https://en.wikipedia.org/wiki/For_the_Benefit_of_Mankind).
• groundzeros2015 13d ago
  The primary motivation for math is not to check off proofs, but to understand the universe. A proof itself is only an articulation of understanding. Traditionally having one was evidence you had an insight. But if a computer generates 10,000 pages of technical goop then we don’t learn anything. For example if tell you P=NP with no other information, it doesn’t change anything. There are mathematicians who believe and act on both conditions. What we hope a proof would reveal is how a verifier could be used to derive the solver (even if doing so was impractical). Why doesn’t the author even mention this and immediately jumps to utility arguments for why the research is important for the government to fund?
  • treszkai 13d ago
    Because it's a poorly written article.
  • infamouscow 13d ago
    > Why doesn’t the author even mention this ... Because the question that belies all of this is whether still makes financial or economic sense in the age of LLMs for tax-payers to fund mathematics research. Up until recently, they've had a true ivory-tower to dismiss such criticism, but as LLMs have demonstrated, that approach won't survive going forward, so pure mathematics are up in arms. They genuinely don't know how to justify their jobs.
    • groundzeros2015 13d ago
      I don’t think this is a key question at all. There are a hundred other academic disciplines that dont provide immediate research utility either. Math was always a few levels removed but somehow sneaks in with engineering and basic science.
• Spacecosmonaut 13d ago
  Mathematicians insist that in many cases the route toward solving a problem is more valuable than solving the problem itself. This may have been true, and may still be true for now, but this seems to implicitly assume that future generations of AI cannot be creative in similar ways that human mathematicians have been. It assumes that the absence of human comprehension during problem exploration loses a valuable aspect of mathematics that cannot be recovered by aiming future AI at solved problems in a naive environment. If we get to a future where all frontier mathematics contributions are by AI. A future where AI displays creativity in ways that expand mathematic exploration similarly to the ways humans have in the past. A future where AI explains frontier mathematics to curious humans. What will have been lost? Perhaps just "The pleasure of finding things out".
  • bayindirh 13d ago
    > What will have been lost? Perhaps just "The pleasure of finding things out". I'll kindly disagree on this front, because when I'm walking a path toward solving a solution, I mark a lot of steps for possible diversions to other paths hence solving adjacent or different problems with the method I have at hand. Currently, AI takes us from A to B, and is improving on that front. However, the paths in science are not lines, but a trees. Methods are cross-pollinated from each other. Human intuition enables this cross-pollination. AI works with a laser focus. Human intuition and resulting wide perspective sow the seeds for solutions in many areas at once.
    • Spacecosmonaut 13d ago
      I recognize that if a document were to be published tomorrow containing solutions to all formulated open problems in mathematics we will have gained very little in mathematical understanding. But surely, if we know that the dead ends of exploring a problem are valuable, we should be able to explore them even if a solution is already known. It just requires that the mathematics community reshapes itself. And it must. Two years from now people might be able to run the computation that solved NS on their Iphone. I'm sure that whatever has been discarded during the NS exploration as a dead end you would be able to rediscover using purpose built tooling in the near future. The purpose of human mathematicians in the medium term might be to explore dead ends, and to provide human insights as context to attack other problems. But whether this type of work will remain necessary in the long term im not sure.
• deleted 13d ago
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• moralestapia 13d ago
  Lol, this really struck a nerve. He has been posting non-stop for about a week now, wrote that lame open letter, gave a talk on it, etc. What a disgrace, but I'm happy he's showing his true self to the public.
  • qnleigh 13d ago
    You realize this is a guest post, right? Terrence Tao didn't write it. He's been using his blog to facilitate discussions about math's future.
• BigTTYGothGF 13d ago
  Lots of deans and college presidents asking themselves the same question.
• FLeXMurphy 13d ago
  I'd like for HN to start tagging posts that are not written by terry tao, but are guest posts, like this one. Considering HN internally already uses AI tools to scan through and read the content to determine if it is AI-generated, I assume this is doable.
• adwinho168 13d ago
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• retrocog 13d ago
  A village builds a clock tower so everyone can glance up at it and know what time it is. The tower helps as people meet more easily, work schedules align, and meals are shared. Over time, fewer people watch the sun and the clock becomes authoritative. When it stops working, nobody knows what time it is. Discord ensues and arguments follow as meetings are missed and people wait impatiently for repairs. An older woman in the village kept baking at dawn and never stopped watching the sun. She never relied on the clock. Villagers gathers at her door and call her wise, for her practice ends up inadvertently helping to re-calibrate the clock once it is repaired. She replies that she is not wise or special and was just going about her usual baking routine.
  • falcor84 13d ago
    I assume this is satire, as obviously they could recalibrate by the sun itself, and the baker is superfluous here.
    • al_borland 13d ago
      This assumes the people fixing the clock know how to tell time based on the movement of the sun. In the story, the baker was the only one left with that ability, as others left the skill behind when the clock became the authority. This problem has been seen when missionaries, or whoever else, try and bring tribes into more modern civilization. They have trouble adapting to modern civilization, but the skill loss during that process makes it almost impossible to go back to the jungle. When skills are lost due to modern technology, it isn’t so trivial to get them back. Look at how much time people have spent trying to figure out how stone was moved in ancient Egypt, for example.
      • falcor84 13d ago
        I am not implying that skill loss does not happen in other situations, but I don't understand how someone would be able to calibrate a clock by the time a baker starts her work day, but not by the time the sun comes up. What am I missing?
• WhatsTheBigIdea 13d ago
  Yet another extremely long and winding "defense" of the mathematics status quo. What's the tldr;? What are the mathematicians arguing for exactly? And against? Totally unclear to me even after chomping through that massive word salad. This all feels very John Henry to me. Why is it not a good thing that we have new tools that can accelerate discovery? Because it disrupts the current order? If you can't make the argument in 100 words, you probably don't have one.
• selicos 13d ago
  The post above this is titled: AI chatbots give wrong answers to financial queries 'most of the time' (ft.com) I think the headline alone makes a reasonable argument based on the AI tools we have today.