Paper: Lean verification of AI autoformalization doesn't guarantee correct proofs, SCI hierarchy argument
burny_tech · x · 2026-10-08
An arXiv paper by Bastounis, Circelli and Hansen targets AI autoformalization — translating natural-language math (e.g. OpenAI's announced Navier-Stokes blow-up proof) into Lean for mechanical verification.
- Key claim: resolving ambiguities in mathematical natural-language text — required for semantically faithful translation — sits arbitrarily high in the Solvability Complexity Index (SCI) / arithmetical hierarchy (SCI = ∞), i.e. harder than any computational problem including Halting (SCI = 1).
- The authors give several real examples of AI mistranslating NL statements and proofs into Lean, causing mismatches with the original argument.
- Conclusion: passing Lean verification may offer no confidence in the original natural-language proof — a direct challenge to the credibility of AI-generated math formalizations.
More from AGI Musings
- Even unsure if Claude is conscious, this user wouldn't gratuitously mistreat AI — kipperrii · 2026-10-09
- 'Moravec's paradox of the economy': hard skills soften as soft skills harden — c_valenzuelab · 2026-10-09
- Commentator: Claude-style dashboards will kill a quarter of data-aggregation SaaS — michalmalewicz · 2026-10-09
- From potato wedding toasts to papal addresses: Mollick marks 4 years of AI's leap — emollick · 2026-10-09
- Astrophysicist builds first complete UV map of the sky with Claude in days, not weeks — AnthropicAI · 2026-10-09
- Commentator: Elliptic Curve Cryptography Could Simply Stop Working — StewartalsopIII · 2026-10-09