OpenAI announced on September 8, 2026, that it had reached a solution to the Navier–Stokes problem, one of the Millennium Prize Problems that had remained open for nearly 90 years. However, the announcement was not treated as a final solution within the mathematical community, because the company has not yet published the proof’s details in a form that would allow researchers to examine it independently. The timing of the announcement also raised questions about how the result was reached.
A Problem Concerning the Motion of Fluids and Gases
The Navier–Stokes equations describe the motion of fluids and gases, including water, air, and blood. The mathematical challenge centers on determining whether these equations always guarantee regular solutions, or whether they can reach a state in which the motion becomes so chaotic that the mathematical solution breaks down.
The Clay Mathematics Institute selected this problem as one of seven problems it called the “Millennium Problems,” offering a $1 million prize for each problem solved according to accepted scientific standards. Therefore, an announcement by a technology company of a potential proof is not sufficient by itself to close the problem; the proof must be made available and reviewed by independent specialists.
An Internal Model and 10,000 Agents
OpenAI said the proof was produced by a group of agents using an internal artificial-intelligence model whose capabilities exceeded those of the GPT-6 Astra model that the company had recently launched. It said it had run about 10,000 artificial-intelligence agents simultaneously. Training of the model used began on August 28, and, according to the company, it demonstrated unprecedented performance on benchmark tests, including mathematics tests.
The company confirmed that it did not intend to claim the $1 million monetary prize, despite describing the result as a major breakthrough in mathematics.
Debate Over Timing and Research Data
The controversy intensified after Tristan Buckmaster, a mathematician at New York University, disclosed research results related to the equations one day before OpenAI’s announcement, in collaboration with Levent Albouy, a researcher at Anthropic. Buckmaster said he contacted OpenAI after learning that the company was aware of the progress made by the two researchers, and that the company had reached a proof through a research path on which he had been working with Albouy using OpenAI’s Codex and Anthropic’s Claude.
This raised questions about whether OpenAI had been able to access Codex sessions or project data. The article reported that the company said the model had not viewed user data, but, according to Buckmaster, it did not provide a clear answer when asked specifically about the possibility that such data had been used in training.
OpenAI, for its part, denied using any specific user’s data to solve the problem, but said it could not rule out the possibility that de-identified data generated through the use of its products had contributed to improving its models. Sebastian Bubeck, one of its technical staff members, also denied that the company had seen Buckmaster and Albouy’s work before it was published, saying that OpenAI’s proof differed from it substantially, including in the proven mathematical results.
What Has Actually Been Established So Far?
The announcement represents an important test of advanced models’ ability to produce mathematical reasoning that goes beyond calculation and the reformulation of known knowledge. But the scientific value of the claim will depend on publication of the proof, the possibility of reexamining it, and researchers’ agreement that it meets the conditions of the Millennium Problem. Until that happens, the most accurate description is that OpenAI has announced a proof it claims to have reached, not a definitively established solution to the Navier–Stokes problem.