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by dataflow 532 days ago
> Part of it is, I think, that "elegance" is flowery language that hides what mathematicians really want: not so much new proofs as new proof techniques and frameworks. An "elegant" proof can, with some modification, prove a lot more than its literal statement. That way, even if you don't care much about the specific result, you may still be interested because it can be altered to solve a problem you _were_ interested in.

Do you feel this could be a matter of framing? If you view the "proof" as being the theorem prover itself, plus the proof that it is correct, plus the assumptions, then whatever capability it gains that lets it prove your desired result probably is generalizable to other things you were interested in. It would seem like a loss if they're dismissed simply because their scratch work is inscrutible.