Comment by cubefox
8 hours ago
And that underestimates how incredibly quickly humans become accustomed to new trends. If an LLM proves P≠NP in year, there is a high chance that few people will care anymore, because at that point LLMs will presumably already have proved multiple Millenium prize and other famous problems, and another "AI Proves Famous Theorem Which Was Even Harder Than The Previous One" headline will be regarded as an old hat.
>If an LLM proves P≠NP in year, there is a high chance that few people will care anymore
P=NP has always been drastically over stated as it's "Importance". It pretty much only exists as "That small technical detail that people with no domain knowledge think is important because youtube videos always focus on the trivial, 101 level cool fact stuff". Math focused CS people of course would always love any proof, but most people expect already that P!=NP, and no proof of that would be very meaningful, as it basically would not change our understanding of anything in the domain currently. It would be nifty, but not earth shattering.
Also the problems LLMs are attacking are resulting in proofs that don't seem particularly enlightening, so that's unfortunate.
However, there's always the tiny tiny chance it is P=NP, and any proof of that, regardless of how insightful it would or would not be, would be worth going fucking insane over. Just knowing that would be meaningful on it's own, and give us limitless work to do, and puts lots of mathematicians in an awkward spot.
I would be considered an AI skeptic because I'm not currently sacrificing myself at the altar of LLM companies, but if LLMs solve P=NP in any direction and even uselessly so, I think that's a good excuse to take days off work and party!