OpenAI Claims a Solution to a Million-Dollar Math Mystery. Two Researchers Are Raising Questions About Credit.
OpenAI‘s claim that an artificial intelligence system has solved one of mathematics’ most famous unsolved problems is being somewhat overshadowed by a dispute over scientific credit, unpublished research and whether AI companies can benefit from the confidential work of researchers who use their products.
The company announced Tuesday that an internal model had produced a proof addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute.
But the announcement followed closely related work by two mathematicians, who have raised questions about how OpenAI developed its result and how their own contributions were treated. The controversy centers on Tristan Buckmaster and Levent Alpöge, who had been investigating related fluid-dynamics questions using AI tools from both OpenAI and Anthropic.
In a statement, Buckmaster said OpenAI accelerated its effort after learning of their progress and subsequently made proposals that could have affected how the researchers received credit.
Buckmaster alleged that one proposal would have allowed him to publish a paper announcing OpenAI’s solution without including Alpöge’s name. OpenAI researcher Sebastien Bubeck disputed that characterization, while CEO Sam Altman defended the company’s work. The allegations remain contested, and there is no established finding that OpenAI improperly used the mathematicians’ research.
I spent much of the weekend talking with the team who did this work. Seb–and everyone else–acted with integrity and generosity throughout.
Initially we believed the other team had also solved the problem. We wanted to collaborate and do a joint release.
When we learned that… https://t.co/XESh5oFHHE
— Sam Altman (@sama) September 8, 2026
The central question of the problem is whether equations describing the movement of fluids, including air and water, always produce smooth solutions, or can those solutions break down in finite time. The equations are fundamental to fields ranging from aerodynamics to weather forecasting. OpenAI says its proof demonstrates a finite-time singularity, a mathematical situation in which a fluid’s calculated velocity becomes unbounded.
The company released a 165-page proof alongside a formalization in Lean, a programming language used to check mathematical arguments. OpenAI said the effort involved as many as 10,000 AI agents over approximately 88 hours and cost millions of dollars in computing resources. The company described the unreleased model as substantially more capable than GPT-6 Astra.
Buckmaster and Alpöge published work concerning the Euler equations, a related model of fluid motion without viscosity. OpenAI’s claimed result addresses the Navier-Stokes problem, which incorporates viscosity. The company has acknowledged the pair’s priority on their Euler work while maintaining that its own proof uses a different approach.
“After the completion of our full project and Lean verification (on September 6th), believing from the rumor [Buckmaster and Alpöge] also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement,” the company wrote in a blog post.
“At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.”
The most consequential question may be what happened to the researchers’ data. Buckmaster said he asked whether OpenAI’s systems had accessed the pair’s Codex sessions, which contained work on their unpublished research.
OpenAI said its researchers and agents did not inspect those prompts or proofs to direct the project. However, the company acknowledged that it could not completely exclude the possibility that de-identified information from their product usage had contributed to model improvements.
That distinction does not establish that the researchers’ work was used to generate the proof. It does, however, expose a broader concern for scientists who rely on commercial AI systems over whether confidential research can indirectly influence future models, and what protections exist when the company operating the tool is also competing to make discoveries.
The scientific milestone itself also requires careful qualification. OpenAI has published a claimed solution, but the mathematical community must still examine the result and determine whether it satisfies the Millennium Prize requirements.
