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@androcat@toot.cat

Post #2438858

2026-04-29 04:29 UTC

@jac@types.pl You're apparently unaware of epistemology. If you have a tool which contains a method for generating text, but no method for generating proofs, and no mathematical understanding for recognizing proofs, then there is no reason to believe it will output proofs. What it will output is stuff that resembles proofs. And since the engines will no doubt have been trained in part on hoaxes, proof-like texts made to be deliberately hard to follow, the generated texts are likely to be very costly to decisively prove wrong. So it's probably garbage (no method involved that would guarantee it makes proofs) but it's hard to know at first glance. This leads to the problem @tao@mathstodon.xyz was outlining: The resources that go into vetting a "generated proof" are the only actual work involved, and since there is a deluge of "probably garbage, but it's hard to know at first glance", this vetting resource would need to be somehow given credit for even bothering. That is if "genAI proofs" should be considered at all, and not disregarded as the probabilistic garbage they are, overall.

Replies (1)

  • @jac@types.pl 2026-04-29 04:54

    @androcat@toot.cat Thanks for the response! I think there's still two counterarguments: 1. For informal proofs, RL prioritizes reasoning that appears valid, and I'm not sure how much they use things like known results 2. Tools like Lean both give feedback on valid proofs enabling systems to learn to produce them, and drastically reduce the checking surface (down to just the definitions).

    Open ##2438859