Comment by hkalbasi

11 hours ago

So we can let the ai generate some math problems based on the solutions found? Other fields (computer science, physics, ...) can generate math problems too.

3 comments

hkalbasi

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mlyle  11 hours ago

There's an infinite number of possible math problems, but the things that make these open problems worthwhile is they're interesting to people who have worked in related areas.

They're good to give to new mathematicians, and they're good to help humans understand the shape of the problem space and relative difficulty with the tools we have.

Cheesing these problems with LLMs gets rid of both the training benefit and our ability to create good related problems. There's an aesthetic part of this, too, that LLMs do not capture.

  • jordanb  10 hours ago

    This kinda reminds me of the guys who decided to industrialize digging up dinosaur fossils, in order to feed the dinosaur fossil collector market. They were amazed that paleontologists were so "inefficient" at finding and digging up dinosaur fossils.

    But from paleontologists' perspective, they go out looking for dinosaur fossils when they have questions that digging up a fossil may answer. The metric they're focusing on isn't tons of fossil mined out of the ground, it's a developing understanding of extinct life.

  • chorizo  10 hours ago

    These open problem solutions often reveal tighter bounds on prior conjectures. Even if the solutions produced are far from elegant and only machine verifiable, we do learn new information. But I agree that just like writing prose and code, brainstorming frontier math proofs is a perishable skill