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Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
A Lean proof that compiles can still differ from the human-written proof it claims to verify.
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Statements accurately formalized, one textbook
A Lean expert's audit of Meta's 26-textbook autoformalisation claim
How it works
Compiling is not faithful
AI translates natural-language proofs into Lean. Success means the code compiles, not that it matches the original argument.
Audit real translations
Small examples and OpenAI's Navier-Stokes Lean code are checked line by line, and ambiguity resolution is analysed in logic.
Mismatches everywhere
The Lean code proves weaker bounds by different arguments. Faithful translation is provably harder than the Halting problem.
From the paper