OpenAI's Navier-Stokes Proof Signals Shift Toward Formal Verification
AI-generated image · US National Wire
The use of Lean 4 to verify complex mathematical proofs in hours rather than thousands of person-hours marks a drastic reduction in the cost of formal methods.
OpenAI recently settled a long-standing question regarding the Navier-Stokes equations in fluid dynamics, as first reported by Hacker News. While the company provided a conventional human-readable proof, it simultaneously released a formal proof using Lean 4.
Writing for Hacker News, John notes that the speed of this verification represents a massive leap in efficiency. He references a 2005 estimate by Henk Barendregt and Freek Wiedijk, which suggested that formalizing a single page of an undergraduate mathematics textbook required approximately 40 work-hours. John calculates that if a research publication requires 20 times the effort of a textbook page, formalizing OpenAI's 166-page paper would have traditionally taken 132,800 person-hours. Instead, OpenAI verified the proof in Lean in just 17 hours.
This shift suggests a broader application for AI-generated formal proofs beyond mathematics. John argues that this capability could be used to verify the correctness of mission-critical algorithms, ensure smart contracts impose specific maximum liabilities, or confirm that security policies are consistent and achieve their intended purpose.