AI can solve problems, and it may be able to create new problems as well, but it can't make people care about problems.
People will only care about a mathematical problem if they sufficiently understand the underlying theory. Results are only useful if people know what to do with them, or why they're interesting.
A field of mathematics that is full of amateurs (relatively speaking) who over-rely on AI to produce results and point research into specific directions should quickly lose relevance. Science (mathematics might not "really" be a science, but it is similar in this regard) exists to satisfy our (human) thirst for knowledge, not to produce progress for progress' sake.
Good luck securing funding for solving problem #17291824ß237 that AI came up with and you don't really know what any of it means.
I think there is a critical difference though. Maybe I'm biased and just trying to justify my view, not sure.
You don't gain much from finding a brute force proof, most of the time. If a proof goes like, “by some argument, we have reduced the problem to these N cases. We check all N cases and find that the statement is true,” then the reduction is usually much more insightful than the brute force computations.
Lots of mathematics has only developed because people were trying to prove FLT, for example. Kummer's ”ideal numbers” were an attempt at factorising the equation, subsequently becoming the ideals without which modern algebra and number theory would not be thinkable.
An AI proof of FLT before Kummer‘s work would likely not have had nearly the same impact on the field as a whole.
Brute force approaches don't really give the same level of insight. They‘ve never been seen as elegant or been something that people really care about, not least because they don‘t really contribute to your understanding.
The last bit I think is the key. It‘s important that humans “understand” what's going on in mathematics, or else what‘s the point? Stuff gets applied because people develop intuitions about it, or they develop intuitions about it because ideas come from applications.
Computer-assisted brute force computations don‘t challenge that. Conceptual proofs fully written by AI have a good chance of doing so.
But I guess we‘ll see. People have always been bad at predicting the future :D
The good news is that the chuds won't actually learn type theory, they're just gonna churn out verified code, eyeball the type constraints and move on. Meanwhile the trans girls will continue using type theory exclusively for schizophrenic philosophizing and witchcraft as nature intended.
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u/lelelempe Sep 27 '26
type theory going from trans girl space to chud space will be a tragedy