# Solution to the Navier-Stokes existence and smoothness problem

**URL:** <https://awg.osdr.space/t/solution-to-the-navier-stokes-existence-and-smoothness-problem/4581>\
**Category:** AWG Discussions\
**Created:** [September 9, 2026, 3:25am UTC](https://awg.osdr.space/t/solution-to-the-navier-stokes-existence-and-smoothness-problem/4581 "2026-09-09T03:25:49Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![angel](https://sea1.discourse-cdn.com/flex001/user_avatar/awg.osdr.space/angel/32/49_2.png) [@angel](https://awg.osdr.space/u/angel)\
**Post date:** [September 9, 2026, 3:25am UTC](https://awg.osdr.space/t/solution-to-the-navier-stokes-existence-and-smoothness-problem/4581/1 "2026-09-09T03:25:49Z")

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![navier-stokes-dark-master](https://us1.discourse-cdn.com/flex001/uploads/osdr/original/2X/e/e0fbc2cf9a817a761bb3d736f18faa8e8ba91006.webp)

An internal OpenAI system produced a proof showing that the dynamics of the Navier-Stokes equations can develop a singularity in finite time. The team has also shared the proof and a formalized version in Lean:

> **[On the Navier–Stokes Millennium Prize Problem](https://openai.com/index/navier-stokes-solution/)**
>
> We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.