This seems to be blowing up and I've had some friends both within and outside of maths ask me what I mean by all of this being a false promise, or by LLMs "reward hacking" publishing incentives, so I wanted to write something addressing that directly.
The current system only really rewards proving something nobody has proved before. Proving something is rewarding *because* when humans do the trial and error , we discover things and develop new ideas and figure out why existing approaches fail and how to mend them. we develop mental models of mathematical objects, we create constructions which get tested over and over to determine if they're useful and flexible, we figure out how to reframe existing proofs in new frameworks and ways of thinking. Counterexamples particularly are often very instructive, and turning counterexamples into obstructions that can be resolved is a major way we advance maths.
The end result of "X is true/false" is NOT the point, but the publishing system has managed to survive despite only rewarding these things because when humans do mathematics we end up doing all the other stuff along the way. It may have had negative effects on expository writing and pedagogy and careers, but it still kinda functioned.
However, I think we have seen these publishing incentives are not surviving contact with LLMs, and the important conceptual work is all being offloaded to people who will not actually get any kudos or credit or career advancement for it, because they didn't prove a novel theorem. They "just" did the fuzzy work of contributing to our shared knowledge, but that work is actually what doing maths means! It's not just creating a library of true/false statements!
(4/3) sorry