If it's gaming the system, then it's much less likely to reliably come up with novel proofs or useful new theoretical ideas.

That would be important, but as far as I know it hasn’t happened (despite how often it’s intimated that we’re on the verge of it happening).

I've seen one Twitter thread from a mathematician who used an llm to come up with a new math result. Both coming up with the theorem statement and a unique proof,iirc.

Though to be clear, this wasn't a one shot thing - it was iirc a few months of back and forth chats with plenty of wrong turns too.

Then he used it as a random text generator, LLM is by far the most configurable and best random test generators we have. You can use that to generate random theorem noise and then try to work with that to find actual theorems, still doesn't replace mathematicians though.

I think we should let the professional mathematician who says the llm helped him be the judge of how and why it helped.

Found the thread: https://x.com/robertghrist/status/1841462507543949581?s=46&t...

From the thread:

> AI assisted in the initial conjectures, some of the proofs, and most of the applications it was truly a collaborative effort

> i went back and forth between outrageous optimism and frustration through this process. i believe that the current models can reason – however you want to interpret that. i also believe that there is a long way to go before we get to true depth of mathematical results.

Yeah, it really does matter if something was reasoned, or whether it appears if you metaphorically shake the magic 8 ball.