Comment by dvt
14 hours 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.
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.
Have we asked AI to create new interesting math problems? XD
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?
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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?
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).
The "proof" is merely an appeal (unreadable program) submitted to a different oracle (Lean).
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.
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> 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.
Yes, the present developments, and the present approach, mean we will not have mathematicians any more.
Your confident re-assertion still doesn't convince me, why do you think so?
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).