[kang]

> The lower bound for contributing to mathematics will now be to prove something that LLMs can’t prove, rather than simply to prove something that nobody has proved up to now and that at least somebody finds interesting.

5.5pro is amazing but this implication might not be true & is the core argument of this piece.

AI will prove all sort of things - interesting, boring & incorrect.

To sort it will be the task of the PhD.

[layer8]

The task of a proof verifier is much simpler than the task of a proof finder (it’s basically equivalent to P vs. NP), and hence the bar for the required skills is lower. Merely verifying proofs isn’t research, and doesn’t impart research skills.

[kang]

Verification on its own is not research, but judgement is research.

"Hey, Prove something a machine can't", sure I can't, "Hey, Say something worth proving & judge it well", ah, now I might have a few unique observation/ideas/curiosities/problems from my having being a human.

Imo, the feeling of intelligence or the process of originality(originativity) test for ai is subjective & is coming down to 4 paths: novel relative to a reference class, valuable within a domain, counterfactually sensitive to internal state and environment, and revisable through learning.

[ianm218]

Verification is generally a much lower bar than solution generation. I don’t think it’s likely sorting out the right from wrong will end up being this huge PhD level effort.

[kang]

Verification & solution generation are both part of problem generation & defining the passing test - judgement.