> “I certainly don't expect the industry to continue to spend millions of dollars to solve problems in mathematics, because there is no profit in it,” Columbia University mathematician Michael Harris wrote in an email to Science. But he worries the highly publicized achievement will be “extremely damaging to mathematics; it convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future.”

LLMs seem particularly suited toward these existence-proof problems. Working mathematicians seem absolutely essential for universally quantified results, still. I strongly doubt, for example, that if Fermat's Last Theorem hadn't been proven three decades ago, that an LLM would be able to do work equivalent to inventing the mathematics as Andrew Wiles did to solve the problem. I have similar doubts about P vs NP, the twin prime conjecture, even the Riemann Hypothesis (unless the latter has at least one counterexample).

And I want to be clear: I'm not downplaying the achievements of these models. This is remarkable! I simply think that the pattern of success is in existence proofs or finding counterexamples, which makes sense based on how LLMs function and are trained.

I only have an undergrad in math, so very little understanding, but I'd be pretty surprised if it couldn't do forall just as well. Like, say it found this counterexample which relies on axial stretching or whatever approach. Then it already knows how that made the proof work, and can use it to try to prove NS has smooth solutions modulo this particular kind of defect (so it could make some statement about cohomology, or some additional constraining equation). Or if that doesn't work, then it can find a counterexample, which we've established it's good at. Then repeat until you've characterized what does work. The various defects, along with being defect free, become definitions. Now you have a theory.

It would be good if someone made a list of allresults obtained with AI so far just to see what kinds of problems AI excels at. Are there any that aren't of the existence-proof type?

Reductively, math can be said to be either problem solving or theory building - it seems the latter is a much harder thing to do right now.

> it convinces decision makers that human mathematicians are obsolete, and it convinces young people that their passion for mathematics has no future

Maybe those things are true, so maybe they should be convinced?

P=NP is for when both AI shops decide they want to go bankrupt LOL