New paper: Lean verification can't guarantee AI's Navier-Stokes proof is correct
pmddomingos · x · 2026-10-08
Pedro Domingos highlights an arXiv paper by Alexander Bastounis, Fabian Circelli and Anders C. Hansen arguing that AI autoformalisation — translating natural-language math into Lean for machine verification, as in OpenAI's announced Navier-Stokes blow-up proof — may offer no confidence in the original argument.
- The paper shows that semantically faithful translation of ambiguous mathematical natural-language text sits arbitrarily high in the Solvability Complexity Index hierarchy (SCI = ∞), informally harder than any computational problem including the Halting problem.
- The authors present multiple real examples of AI mistranslating natural-language statements and proofs into Lean, producing mismatches between verified formal versions and the original proofs.
- Bottom line: passing Lean verification does not guarantee the natural-language proof is correct, challenging the methodology behind AI-generated mathematical proofs.
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