OpenAI announced on September 8, 2026, that it had found 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, 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 the path by which the result was reached.
A problem concerning the movement of fluids and gases
The Navier–Stokes equations describe the movement 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” and offered 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 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 that 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 approximately 10,000 artificial intelligence agents simultaneously, while training of the model used began on August 28 and, according to the company, demonstrated unprecedented performance in benchmark tests, including mathematics tests.
The company confirmed that it does not intend to claim the $1 million prize, despite describing the result as a significant breakthrough in mathematics.
Controversy over timing and research data
The controversy escalated after Tristan Bakmeister, a mathematician at New York University, disclosed research results related to the equations one day before OpenAI’s announcement, in collaboration with Levant Albuge, a researcher at Anthropic. Bakmeister said that 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 Albuge using OpenAI’s Codex and Anthropic’s Claude.
This raised questions about whether OpenAI had managed to access Codex sessions or project data. The article reported that the company said the model had not viewed user data, but, according to Bakmeister, it did not provide a clear answer when asked specifically about the possibility of using that data in training.
For its part, OpenAI denied using any specific data belonging to any user 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 Bobek, one of its technical staff members, also denied that the company had seen Bakmeister and Albuge’s work before it was published, saying that OpenAI’s proof differs 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 computation and the reformulation of known knowledge. However, 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 that the company claims to have reached, not a definitively proven solution to the Navier–Stokes problem.