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Joined 3 years ago
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Cake day: August 16th, 2023

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  • My understanding is that they published a machine-checkable proof (Lean).

    There’s already valid epistemological question about whether proofs that are only machine-checkable are the same quality of knowledge as traditional proofs. For instance, the 1976 proof of the four-color theorem was controversial in part because it was too long to be read by a human.

    Another part of the argument is that the foundations are quicksand: proof checkers include unverified code (read: potentially buggy) and run atop unverified OS kernels on a likely proprietary CPU! (Personally, I think if you can understand the theorem statement, it’s safe to delegate the drudgery of the proof-checking to a computer. If two different systems agree, that’s good enough for me. But I’m neither a mathematician nor a philosopher.)

    These AI generated proofs push the boundary further because humans participated even less in the formalization and proof development.