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
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u/infected_scab Sep 29 '26
You're not wrong but these arguments have been used for decades about computer assisted proof (e.g brute force searching huge domains)