GoKawiilOpenAI's Navier-Stokes proof included a Lean 4 formal verification, done in 17 hours
Alongside its human-readable proof resolving a longstanding Navier-Stokes question, OpenAI also released a machine-checkable Lean 4 formal proof, completed in about 17 hours. The author contrasts this with historical estimates that formalizing research-level math could take tens of thousands of person-hours by hand.
GoKawiil's interpretation of the reporting above, not reported fact.
If AI can compress formal verification time by roughly four orders of magnitude, it changes what's practical not just in pure math but in any domain requiring rigorous, checkable logic, such as security policy verification or software correctness. This shift could make formal verification a routine step rather than a rare, expensive luxury.
- OpenAI paired its Navier-Stokes proof with a Lean 4 formal verification finished in 17 hours.
- Manual formalization historically took about 40 hours per textbook page, far more for dense research papers.
- Cheap formal verification could extend beyond math to areas like security policy and software correctness checks.
The Hitchhiker's Guide to Logical Verification (Lean 4) — If the article's talk of Lean 4 formal proofs has you curious, this is the standard hands-on introduction to writing and checking proofs in Lean 4. It walks you from basic tactics to real formalization, so you can see for yourself what those machine-verified Navier-Stokes proofs actually look like.
See The Hitchhiker's Guide to Logical Verification (Lean 4) on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.Source: johndcook.com, 2026-09-10
Published there as: “The part of Navier-Stokes no one is talking about”
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