Comment by nilkn
4 hours ago
I actually think it's the opposite: Lean proofs and autoformalization make it very easy to announce proofs alongside proofs of the correctness of those proofs (Lean certificates). It's not an absolutely fool-proof combination (the Lean kernel could still contain bugs), but it does immediately attach a very substantial degree of credibility to the result.
And that I think is essential to why some of the world's leading mathematicians are taking this so hard. In a world where we "merely" have AI systems capable of superhuman informal reasoning, verification, correctness, and acceptance could still only be conferred or anointed by human mathematicians. But a world that combines superhuman informal reasoning with superhuman autoformalization is a fundamental shakeup in the institutional order.
The recent proof of Fermats Last Theorem is interesting: it is (iirc) 13 million lines of lean code. And type-checking takes 5 hours or so on a pretty beefy machine. I cannot independently verify the proof, and I have to take Anthropics word for it that it actually type-checks.
That seems like a red herring. Have you independently verified the human generated proof of FLT? Surely someone else will try to verify Anthropic's formalization on different hardware. Plus, it seems likely that FLT formalizations will improve / get shorter over time, requiring less compute. And computers (and type-checkers) will continue to get faster over time as well. So maybe in 5 years you could own a computer fast enough to verify a/the proof in say a week, instead of 5 hours.