New paper: Lean verification doesn't guarantee AI proofs are correct, challenging OpenAI's Navier-Stokes claim
anshulkundaje · x · 2026-10-08
A new arXiv paper by Bastounis, Circelli and Hansen, titled Navier-Stokes lost in translation, challenges the practice of using Lean formal verification to endorse AI-generated mathematical proofs — including OpenAI's announced proof of blow-up of Navier-Stokes solutions via autoformalisation.
- The authors show the formalised Lean proof does not correspond to the written-paper proof of blow-up: passing machine verification says nothing about the original natural-language argument.
- Theoretically, resolving ambiguities in mathematical NL text — required for semantically faithful translation — sits arbitrarily high in the Solvability Complexity Index hierarchy (SCI = ∞), making faithful AI autoformalisation harder than any computational problem, including the Halting problem.
- They document multiple practical cases of AI mistranslating NL statements and proofs into Lean, producing mismatches.
Takeaway: autoformalisation plus Lean verification may offer little to no confidence in the correctness of the underlying natural-language proof.
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