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 about 90 years. However, the announcement was not treated as a final solution within the mathematical community, as the company has not yet published the details of the proof in a way 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 prize of $1 million for each problem solved according to accepted scientific standards. Therefore, an announcement by a technology company of a possible proof is not sufficient on its own 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 exceed those of the GPT-6 Astra model recently launched by the company. It said it had run about 10,000 artificial intelligence agents simultaneously, while training of the model used began on August 28. According to the company, the model demonstrated unprecedented performance on benchmark tests, including mathematics tests.
The company confirmed that it did not intend to claim the $1 million prize, despite describing the result as a significant 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 Albughe, 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 he had been pursuing with Albughe 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.
For its part, OpenAI denied using any specific user’s data to solve the problem, but said it could not rule out the possibility that anonymized 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 Albughe’s work before it was published, saying that OpenAI’s proof differs substantially from it, including in the mathematical results established.
What Has Actually Been Established So Far?
The announcement represents an important test of advanced models’ ability to produce mathematical reasoning that goes beyond computation 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 requirements of the Millennium Problem. Until that happens, the most accurate description of what OpenAI announced is a proof the company claims to have reached, not a definitively established solution to the Navier–Stokes problem.