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by integralid 77 days ago
>This is literally the same thing as

No.

>You can

Not right now, right? I don't think current AI automated proofs are smart enough to introduce nontrivial abstractions.

Anyway I think you're missing the point of parent's posts. Math is not proofs. Back then some time ago four color theorem "proof" was very controversial, because it was a computer assisted exhaustive check of every possibility, impossible to verify by a human. It didn't bring any insight.

In general, on some level, proofs like not that important for mathematicians. I mean, for example, Riemann hypothesis or P?=NP proofs would be groundbreaking not because anyone has doubts that P=NP, but because we expect the proofs will be enlightening and will use some novel technique

1 comments

Right, in the same way that programs are not opcodes. They're written to be read and understood by people. Language models can deal with this.

I'm not sure what your threshold for "trivial" is (e.g. would inventing groups from nothing be trivial? Would figuring out what various definitions in condensed mathematics "must be" to establish a correspondence with existing theory be trivial?), but I see LLMs come up with their own reasonable abstractions/interfaces just fine.