Math is, of course, an ideal field for AI to work in. However, I find this quote revealing:
"It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results. Basically the paper is so horribly written that it’s impossible to read it without AI help."
This makes one wonder how many of the proofs are actually valid, and how many are just impenetrable hallucinations.
> Math is, of course, an ideal field for AI to work in.
I find it interesting that you state this as obvious. When ChatGPT was introduced four years ago, the argument was that language was fuzzy and probabilistic and that LLMs would thereby never work in math.
It's not hard to tie a deterministic process to any stream of output. The thing "hand waves" a proof and some other process exhaustively searches for either lean operations or some other math-manipulator operations that may create a real proof. The processes go back and forth. A proof is a verifiable string at the end of the day and this is better-than-pure-brute-strategy search strategy guided by heuristics from math literature.
I think someone asked here a bit ago whether other search strategies using OpenAI levels of compute have been tried and think the answer is no (even 3 hours of present GPU computer I think is vast compared to anything available 10 years ago, say).
The proofs could be optimized for human consumption.
OpenAI could optimize each proof for fewest theorems, low branching, or short dependency chains.
OpenAI could have an adversarial network enforce that proofs look human.
OpenAI could spend a couple more machine hours per paper with the prompt "edit for clarity".
"It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results. Basically the paper is so horribly written that it’s impossible to read it without AI help."
This makes one wonder how many of the proofs are actually valid, and how many are just impenetrable hallucinations.