Looking at the recent discussions on Hacker News about AI solving difficult problems, it seems there are specific types of mathematical challenges where AI truly excels.

It appears to be relatively good at problems where finding the initial answer is difficult, but verifying whether a candidate answer is correct is easy. In particular, AI feels very strong in matching-type problems, almost like fuzz testing. As seen in Terence Tao's conversations, it has a massive advantage in rapidly substituting and testing various models.

Given these strengths, I feel it would be highly effective for problems like the Hadamard matrix of order 668, the Lonely Runner conjecture, and the Graceful Tree conjecture.

Perhaps the unsolved problems I mentioned will be cracked in the near future? It is fascinating.

> Hadamard matrix of order 668

Solved? https://epoch.ai/frontiermath/open-problems/hadamard

It's honestly just good at math. Even at theory building i wouldn't put it below 90 percentile. Just on some things it's superhuman already and some not yet.

> appears to be relatively good at problems where finding the initial answer is difficult, but verifying whether a candidate answer is correct is easy.

The opposite can happen too, as Knuth’s recent experience showed. The system suggested an unusual approach that he explored.

Yes, LLM is excellent at optimizing exhaustive search algorithms into "representative" search algorithm, by generating heuristic classifications at high scale.

Yep. That's exactly the case.

External graph state/rudimentary planner + LLM proposer + cheap verifier gets so much done.

It sounds like the same class of application as vulnerability finding: try a million dumb things, and one of them can work. No human would try all one million, but a big enough computer can.