If you think about it, it’s extremely odd that humans can find proofs so quickly and efficiently. From Timothy Gowers & Turing, we know that to find a proof for anything, it has to be NP time, but humans regularly do it in “clean” ways, how is this possible?

Gowers has this idea that humans don’t backtrack a lot, that we don’t need to do this unnaturally large search over a hypothesis space to find good ideas, how true is that? Is it true that we develop better models through education and playing around?

I’m not certain that I agree that a large search over things to get a better representation is a necessarily bad idea of how this works. Although, if we think that math skills may have come out of some generalization or transfer learning, then could we test something similar with LLMs? What kinds of tasks have you transfer skills to math?