Did OpenAI race ahead on Navier-Stokes? Mathematicians raise serious questions

OpenAI says an internal AI model has solved the Navier-Stokes Millennium Prize Problem, one of mathematics’ biggest open questions. The claim has triggered a dispute after researchers raised concerns over timing, unpublished work and who deserves credit for the breakthrough.

OpenAI says an internal AI system has produced a solution to the Navier-Stokes existence and smoothness problem, one of mathematics’ seven Millennium Prize Problems. The company released a written proof and a formal version in Lean on September 8, saying its result shows that the equations describing fluid motion can develop a singularity in finite time.

The mathematical claim could be historic if it survives expert scrutiny. Yet the story has quickly become tangled in a dispute over research priority, unpublished work and whether OpenAI raced ahead after learning that mathematicians Tristan Buckmaster and Levent Alpöge were closing in on related results. OpenAI denies using their unpublished proof or prompts.

What did OpenAI actually do?

OpenAI says it used an unreleased model that is more capable than GPT-6 Astra.

The company initially put more than 1,000 AI agents on a simplified version of the problem. It later increased that effort to as many as 10,000 agents. OpenAI researcher Sébastien Bubeck said the final solution was completed and formalised in Lean after a huge computing effort that cost “in the millions of dollars”.

Lean matters here. It is a formal proof system that can mechanically check whether a mathematical argument follows........

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