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> I don't think that's true. Often, to come up with a proof of a particular theorem of interest, it's necessary to invent a whole new branch of mathematics that is interesting in its own right e.g. Galois theory for finding roots of polynomials. If the proof is automated then it might not be decomposed in a way that makes some new theory apparent. That's not true of a simple calculation.

Ya, so? Even if automation is only going to work well on the well understood stuff, mathematicians can still work on mysteries, they will simply have more time and resources to do so.

by ndriscoll10 hours ago|

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This is literally the same thing as having the model write well factored, readable code. You can tell it to do things like avoid mixing abstraction levels within a function/proof, create interfaces (definitions/axioms) for useful ideas, etc. You can also work with it interactively (this is how I work with programming), so you can ask it to factor things in the way you prefer on the fly.

by integralid7 hours ago|

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>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