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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
by 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 agoMathematics 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 agoI 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 agoYes, 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 agoWhat is it, if not an art?
- daze42 8d agoA science?
- adastra22 8d agoTruth.
- BeetleB 7d agoWhat is truth if we are free to pick our axioms? The universe is either Euclidean or not. If it were, how can theorems on non-Euclidean geometry be true?
- gre 7d agoYou pick your axioms and you see what must be true. With math and logic, we can reason about any possible universe even though we live in only one of them.
- wrsh07 7d agoYes, open source isn't art either, yet my point is that the same principle applies to both There are many ways to stop progress and productivity
- wrsh07 7d agoImportantly, which mathematicians will understand deep useful math? Who will actually care about the knowledge we can generate at will?
- unified101 8d agoHave we asked it new interesting math problems, after studing some space for an evening or a day?