OpenAI presents solution to the Navier–Stokes Millennium Prize problem
OpenAI has announced that an internal AI system has presented a solution to the Navier–Stokes problem. The proof has been verified using the Lean tool and concerns one of mathematics' most enduring unsolved questions.
What happened?
On 8 September 2026, OpenAI announced that an internal AI system has developed a solution to one of the Millennium Prize problems. The solution demonstrates that the dynamics of the Navier–Stokes equations for fluid motion can develop a singularity within finite time. The company is publishing both a written account of the proof and a formal verification using the proof assistant Lean.
Key facts
| Publiceringsdatum | 8 september 2026 |
|---|---|
| Problemområde | Navier–Stokes-ekvationerna |
| Verifieringsverktyg | Lean |
”This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time.”
”The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years.”
Why it matters
The Navier–Stokes problem was designated by the Clay Mathematics Institute in 2000 as one of seven Millennium Prize problems, but the question of whether three-dimensional fluid motion can break down has remained unsolved for approximately 90 years. If the proof is accepted, it represents a breakthrough for the use of advanced AI models in solving complex and theoretical scientific problems.
Who is affected?
The news is primarily relevant to researchers in mathematics, physics, and computer science working on fluid mechanics and AI-assisted theorem proving. Developers and academic institutions now have access to both the theoretical documentation and the Lean code for review.
What else you should know
The initiative highlights the use of formal proof assistants like Lean to verify mathematics performed by artificial intelligence. OpenAI emphasises that the purpose of this development is to provide researchers with tools to drive scientific progress.
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