On September 8, 2026, OpenAI stated that its internal AI system had solved one of the seven Millennium Prize Problems — the existence and smoothness of solutions to the Navier–Stokes equations.
According to the company, the proof shows that a smooth fluid at rest under a smooth force can develop a singularity in finite time, while energy remains finite.
The solution was obtained with thousands of AI agents working for approximately 88 hours and was formalized in Lean.
The announcement immediately sparked controversy in the mathematical community.
New York University professor Tristan Buckmaster and Anthropic researcher Levent Alpöge had shortly before published results on related problems that were considered important steps toward solving the Navier–Stokes problem.
Buckmaster expressed concern that OpenAI might have learned of their work's direction and accelerated its own efforts using a similar approach.
The company denied accusations of accessing others' data or drafts, stating it acted based on public rumors of progress on other Millennium problems.
How exactly the AI agents arrived at the proof and whether it can be considered an independent breakthrough is now being discussed by mathematicians and AI experts.
It is interesting whether this episode will affect researchers' trust in using commercial models for work on unpublished results.
OpenAI emphasized that it does not intend to claim the one-million-dollar prize from the Clay Institute.
The event became another example of how rapidly AI capabilities in mathematics are advancing, but it also raised questions about ethics and authorship in human–machine collaboration.
