New arXiv paper: Lean verification of AI math proofs doesn't guarantee the natural-language argument is correct
asusarla · x · 2026-10-08
An arXiv paper (2610.08144) by Bastounis, Circelli, and Hansen directly challenges the verification behind OpenAI's announced proof of Navier-Stokes blow-up:
- Core claim: autoformalisation — AI translating natural-language math into Lean for mechanical verification — offers no confidence in the original NL argument, because semantically faithful translation is itself intractable
- Theoretical result: resolving ambiguities in mathematical NL text sits at the top of the Solvability Complexity Index hierarchy (SCI = ∞), formally harder than any computational problem including the Halting problem
- Evidence: multiple real examples of AI mistranslating NL statements and proofs into Lean, producing mismatches between the formal and informal arguments
The paper was shared at Gary Marcus with a "Terence Tao shitposting" jab. A substantive counter to the "Lean-verified means correct" narrative.
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