---
title: "OpenAI's Navier-Stokes Proof in Lean 4: A Revolution"
description: "Via Hacker News: Article URL: [https://www.johndcook.com/blog/2026/09/09/formal-method-revolution/](https://www.johndcook.com/blog/2026/09/09/formal-method-r..."
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---

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### OpenAI's Navier-Stokes Proof in Lean 4: A Revolution

Hacker News • September 10, 2026 at 5:22 PM ET

[×](/dev?tab=hacker-news)

Yesterday OpenAI announced a proof settling a long-standing question about the Navier-Stokes equations. But an overlooked aspect: they also posted a Lean 4 formal proof alongside the human-readable one.

Until recently, formal proofs were tedious. In 2005, **Henk Barendregt** and **Freek Wiedijk** estimated one work-week to formalize one page of an undergraduate math textbook. Research papers are denser. Formalizing OpenAI's **166-page** paper might take **132,800** person-hours. OpenAI verified their proof in Lean in **17 hours**.

Lowering the cost by four orders of magnitude is revolutionary. I've used AI to generate formal proofs for a blog post; I wouldn't dream of doing that if it cost a week's salary.

Formal verification applies beyond math: security policies, smart contracts, mission-critical algorithms. These are easier and have clearer ROI.

[Read original article](https://www.johndcook.com/blog/2026/09/09/formal-method-revolution/)

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