4 ms·

> Mathematicians will be less likely to work on a problem if there is a solution Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle exis

by dvt 8d ago

> Mathematicians will be less likely to work on a problem if there is a solution Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle existed which could answer any question truthfully. Let's ignore the mechanics of this for now, but it could say things like "the Riemann hypothesis is False" or whatever and we would take it as gospel. Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? I genuinely don't think so.

_alternator_ 8d ago
I mean, the oracle doesn't really seem so hypothetical right now. And clearly it's going to drastically change these fields, and mathematics, particularly pure mathematics, must change most of all in order to adapt to the existance of a math oracle (or something close to it).
nafey 8d ago
I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems. FWIW this is my understanding of his argument and I am not a mathematician.
- gre 8d ago
  Have we asked AI to create new interesting math problems? XD
  - wrsh07 8d ago
    Yes, many mathematicians have. As Tao points out, merely suggesting new open questions isn't really sufficient. Part of what gives these problems their fame is their notoriety, their difficulty, the fact that many prodigious mathematicians have spent an evening or week or month or several years studying it. It wouldn't be as interesting if it had just been solved by the fifth random mathematician who considered it Notably, gardening a new field of study in math is somewhat nontrivial. You have to introduce the field, illustrate some relevance or connections, and then - and this is key - not solve all of the low-hanging fruit yourself! Because you need somebody else to become an expert in that particular field. The analog in programming is: if a large company merely open sources a product that's decent but not great and in a language nobody wants to maintain, but they don't commit to maintaining it themselves. Suddenly there's a bit of a vacuum because in order to provide something of value, you either need to: 1. Implement something more complete than was initially open sourced 2. Or maintain something in a horrendous language while incrementally improving it and keeping it relevant 3. Or rewrite it into a tolerable and maintainable modern language. What the large company has done is create a vacuum in the tool space where you now require extreme motivation to get someone else to step in. Note that in this scenario, in 2026, it's actually not such a big deal. I think several recent models could happily translate it into a more maintainable language themselves or happily maintain it in the original crufty one. And so the question is: which parts of this analogy are true in math, too?
    - adastra22 8d ago
      Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.
      - wrsh07 6d ago
        I think everyone is conflating a few things: * (1) Mathematics, the true things known by humans * Mathematics, the things that are true * (3) Mathematics, the institution which gets funding and manages resources to expand and maintain 1 AI agents can discover more true things, but that doesn't necessarily expand 1 and it might undermine 3 If someone is worried about 3 and you're talking about 2, then you are talking past each other
        formerlyknownas 6d ago
        Yes, these things are definitely being conflated and there's a fourth conflated thing I think Tao is particular getting at: (4) Mathematics, the community which is a living system that decides what is interesting, constructs shared frameworks, transfers ideas between domains, develops taste, teaches new mathematicians, and continually emphasizes what counts as important mathematics, especially in it's overall value to humanity. This is the level in which theory building, simplification, integration and applications are built on. Contributing meaningfully here requires much more than generating solutions - it requires direction and restraint. Tao seems to be saying that this direction and restraint is the scarce resource that drives mathematical progress, not problem-solving ability. And AI is not only insufficient at it, but results generated by AI are destroying human ability to excercise this resource. This seems similar to another problem AI sucks at - drafting legal agreements. Despite being great at evaluating, interpreting, and comparing legal agreements it fails amazingly at drafting them. This is because what you don't say/do is vastly more important than what you do say/do. And AI is great saying and doing things, it's the selection based on implied values that it struggles with.
      - BeetleB 8d ago
        What is it, if not an art?
- morpheos137 8d ago
  The sphere of human comprehensible mathematics is finite. Once everything is solve it is not necessary to advance the field. The recurring error her is to say ai is not the product of human effort but another agent. Ai is human. Ai may well be speeding up human comprehension of math to its limits in which case there is no further need to advance the field and mathematicians might need to get a job. Why is this a bad thing?
  - lanstin 7d ago
    I have never heard this theory that mathematics is finishable before.
monktastic1 8d ago
But this oracle doesn't just say true / false. It also gives a proof. That makes it much less exciting (not to mention beneficial for your career) to find another one (or even worse, the same one).
- gowld 8d ago
  The "proof" is merely an appeal (unreadable program) submitted to a different oracle (Lean).
  - unified101 8d ago
    What do u think lean is? That's like saying a program that works, is inscrutable because it appeals to the oracle of "code test cases" to prove itself correct. You're either being intentionally obtuse, or unintentionally ignorant.
    - yorwba 8d ago
      Have you tried to read the Lean proofs produced for any of the recent high-profile results? They're extremely long, terribly structured, and don't indicate which parts are restating known results from literature and which are unique to the proof at hand. That's what makes them inscrutable. It's similar to Mochizuki claiming to have proved the ABC conjecture, with a proof depending on ideas developed over a large number of obscure papers, that required mathematicians to spend a lot of time before they felt they understood it well enough to point out flaws. If AI solves all famous open problems and the non-famous ones, too, without advances in the readability of their output, there'll still be some work to do to digest and rearrange the proofs for human consumption. During that process, the mathematician may well get some new ideas...
      - benibela 7d ago
        >It's similar to Mochizuki claiming to have proved the ABC conjecture Now I wonder if someone could port his proof to Lean
      - 7d ago
applicative 8d ago
Yes, the present developments, and the present approach, mean we will not have mathematicians any more.
- dvt 8d ago
  Your confident re-assertion still doesn't convince me, why do you think so?
onetimeusename 8d ago
> Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? In the case of mathematicians, I think not as researchers. What would a research mathematician do? I don't think there would be any reason to try to gain insight from proofs that AI made for the sake of understanding. I don't see what that would achieve besides just retaining extremely niche knowledge (which AI or the oracle already does). The whole point of having that knowledge was to build toward novel work which the AI/oracle does. Also, the time spent and difficulty understanding them could be very high but with no payoff besides just understanding them because the AI/oracle would be used to solve all the problems anyway.

by dvt 8d ago

_alternator_ 8d ago

I mean, the oracle doesn't really seem so hypothetical right now. And clearly it's going to drastically change these fields, and mathematics, particularly pure mathematics, must change most of all in order to adapt to the existance of a math oracle (or something close to it).

nafey 8d ago

I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems. FWIW this is my understanding of his argument and I am not a mathematician.

gre 8d ago
Have we asked AI to create new interesting math problems? XD
- wrsh07 8d ago
  Yes, many mathematicians have. As Tao points out, merely suggesting new open questions isn't really sufficient. Part of what gives these problems their fame is their notoriety, their difficulty, the fact that many prodigious mathematicians have spent an evening or week or month or several years studying it. It wouldn't be as interesting if it had just been solved by the fifth random mathematician who considered it Notably, gardening a new field of study in math is somewhat nontrivial. You have to introduce the field, illustrate some relevance or connections, and then - and this is key - not solve all of the low-hanging fruit yourself! Because you need somebody else to become an expert in that particular field. The analog in programming is: if a large company merely open sources a product that's decent but not great and in a language nobody wants to maintain, but they don't commit to maintaining it themselves. Suddenly there's a bit of a vacuum because in order to provide something of value, you either need to: 1. Implement something more complete than was initially open sourced 2. Or maintain something in a horrendous language while incrementally improving it and keeping it relevant 3. Or rewrite it into a tolerable and maintainable modern language. What the large company has done is create a vacuum in the tool space where you now require extreme motivation to get someone else to step in. Note that in this scenario, in 2026, it's actually not such a big deal. I think several recent models could happily translate it into a more maintainable language themselves or happily maintain it in the original crufty one. And so the question is: which parts of this analogy are true in math, too?
  - adastra22 8d ago
    Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.
    - wrsh07 6d ago
      I think everyone is conflating a few things: * (1) Mathematics, the true things known by humans * Mathematics, the things that are true * (3) Mathematics, the institution which gets funding and manages resources to expand and maintain 1 AI agents can discover more true things, but that doesn't necessarily expand 1 and it might undermine 3 If someone is worried about 3 and you're talking about 2, then you are talking past each other
      - formerlyknownas 6d ago
        Yes, these things are definitely being conflated and there's a fourth conflated thing I think Tao is particular getting at: (4) Mathematics, the community which is a living system that decides what is interesting, constructs shared frameworks, transfers ideas between domains, develops taste, teaches new mathematicians, and continually emphasizes what counts as important mathematics, especially in it's overall value to humanity. This is the level in which theory building, simplification, integration and applications are built on. Contributing meaningfully here requires much more than generating solutions - it requires direction and restraint. Tao seems to be saying that this direction and restraint is the scarce resource that drives mathematical progress, not problem-solving ability. And AI is not only insufficient at it, but results generated by AI are destroying human ability to excercise this resource. This seems similar to another problem AI sucks at - drafting legal agreements. Despite being great at evaluating, interpreting, and comparing legal agreements it fails amazingly at drafting them. This is because what you don't say/do is vastly more important than what you do say/do. And AI is great saying and doing things, it's the selection based on implied values that it struggles with.
    - BeetleB 8d ago
      What is it, if not an art?
morpheos137 8d ago
The sphere of human comprehensible mathematics is finite. Once everything is solve it is not necessary to advance the field. The recurring error her is to say ai is not the product of human effort but another agent. Ai is human. Ai may well be speeding up human comprehension of math to its limits in which case there is no further need to advance the field and mathematicians might need to get a job. Why is this a bad thing?
- lanstin 7d ago
  I have never heard this theory that mathematics is finishable before.

monktastic1 8d ago

But this oracle doesn't just say true / false. It also gives a proof. That makes it much less exciting (not to mention beneficial for your career) to find another one (or even worse, the same one).

gowld 8d ago
The "proof" is merely an appeal (unreadable program) submitted to a different oracle (Lean).
- unified101 8d ago
  What do u think lean is? That's like saying a program that works, is inscrutable because it appeals to the oracle of "code test cases" to prove itself correct. You're either being intentionally obtuse, or unintentionally ignorant.
  - yorwba 8d ago
    Have you tried to read the Lean proofs produced for any of the recent high-profile results? They're extremely long, terribly structured, and don't indicate which parts are restating known results from literature and which are unique to the proof at hand. That's what makes them inscrutable. It's similar to Mochizuki claiming to have proved the ABC conjecture, with a proof depending on ideas developed over a large number of obscure papers, that required mathematicians to spend a lot of time before they felt they understood it well enough to point out flaws. If AI solves all famous open problems and the non-famous ones, too, without advances in the readability of their output, there'll still be some work to do to digest and rearrange the proofs for human consumption. During that process, the mathematician may well get some new ideas...
    - benibela 7d ago
      >It's similar to Mochizuki claiming to have proved the ABC conjecture Now I wonder if someone could port his proof to Lean
    - 7d ago

applicative 8d ago

Yes, the present developments, and the present approach, mean we will not have mathematicians any more.

dvt 8d ago
Your confident re-assertion still doesn't convince me, why do you think so?

onetimeusename 8d ago

> Does this mean that we wouldn't have mathematicians or physicists or computer scientists or biologists anymore? In the case of mathematicians, I think not as researchers. What would a research mathematician do? I don't think there would be any reason to try to gain insight from proofs that AI made for the sake of understanding. I don't see what that would achieve besides just retaining extremely niche knowledge (which AI or the oracle already does). The whole point of having that knowledge was to build toward novel work which the AI/oracle does. Also, the time spent and difficulty understanding them could be very high but with no payoff besides just understanding them because the AI/oracle would be used to solve all the problems anyway.