OpenAI says it has solved the Navier-Stokes problem, one of the great unsolved questions in mathematics. But there is debate about the paternity of the company.
OpenAI has announced that one of its artificial intelligence models has solved one of the most difficult mathematical dilemmas ever, the one concerning the understanding of the Navier-Stokes equations: the question is considered essential for the study of the movement of fluids and for the complete description of the phenomenon of turbulence.
But while the company described the achievement as “a milestone for AI research”, praising the extraordinary computing power used to decipher the problem, a dispute arose in the mathematical community over the authorship of the discovery.
What are Navier-Stokes equations
The Navier-Stokes equations, named after the French engineer and scientist Claude-Louis Navier and the English mathematician George Stokes, are fundamental equations for the hydrodynamics of compressible fluids, that is, fluids whose density can vary significantly due to changes in pressure or temperature.
They describe how the velocity of a fluid changes due to inertia, pressure, viscosity and external forces. They are used to describe how the air around an airplane, water in a pipe, blood in arteries, and countless other fluids move in their systems; they are used in aircraft design and weather forecasting.
Understanding these equations is considered one of the seven problems for the millennium, the most difficult traditional mathematical problems to solve and with profound economic/practical implications established by the Clay Mathematics Institute, a foundation based in Cambridge, Massachusetts, which works to increase knowledge of mathematics.
For the resolution of these dilemmas that seem to resist any attempt at a solution, the institute has offered a cash prize, which amounts to one million dollars for each question. So far only one of these problems – the Poincaré conjecture – has been solved (by the Russian mathematician Grigori Perelman).
What result does OpenAI want?
In a press conference on September 8, 2026, OpenAI said it had demonstrated that Navier-Stokes equations can collapse over time: that is, there are situations in which these equations stop making sense and start producing senseless results, which mathematicians call “blow-up” scenarios (literally explosion, sudden rupture). Whether this could happen was one of the questions posed by the millennium problem that concerns them.
“Our demonstration shows that there are fluids which, despite starting in absolutely normal conditions, based on the Navier-Stokes equations actually reach infinite speed in a finite time,” said Ven Chandrasekaran, OpenAI computer scientist at a press conference.
Since such behavior is physically impossible for a real fluid – such as a liquid or a gas – this suggests that, under certain circumstances, the equations may not accurately reflect physical reality.”
Two hundred years of doubts resolved at record speed
In describing the discovery, OpenAI explained, without providing details, that it had used “a significantly higher performing internal model of GPT-6 Astra”, which would have demonstrated unprecedented performance in benchmark (software acceptance testing) of the company and that he would be trained starting from August 28th. The model would initially respond to a simplified version of the problem, fielding 1000 AI agents (i.e. autonomous software systems) that worked for 50 hours.
But on September 1, after hearing rumors that two millennium problems had been solved, OpenAI scientists decided to work on the complete Navier-Stokes equation and increased their computing power, eventually employing 10,000 AI agents to solve the problem. This operation, the solution to a problem that has puzzled the best mathematical minds for two centuries, took the AI only 11 hours, but with calculation costs of around 15 million dollars.
An ongoing academic dispute
The competition entries admitted by OpenAI refer to the work of two scientists humansTristan Buckmaster, a mathematician at New York University, and Levent Alpoge, of the AI company Anthropic, a rival of OpenAI and parent of the LLM Claude. A few hours before OpenAI’s announcement, the two had released their work through an online document, the resolution of three significant intermediate steps considered important for solving the Navier-Stokes problem. The two scientists said they have been collaborating for months and have received “a remarkable helping hand” from AI, including using Anthropic’s LLM and OpenAI.
However, when OpenAI claimed to have done a more complete job, essentially exploiting only the autonomous contribution of AI agents, Buckmaster accused the company of opacity: the giant would have used the same approach used by Buckmaster and Alpöge in the previous months, without providing details on how it achieved the result and pursuing the same logical path followed by the two mathematicians in the previous months.
The not-so-veiled accusation is that it exploited the work of the pair of scientists stored in OpenAI’s cloud to train its AI agents. And for not having given credit to their contribution, thanks to the fact that the rival company Anthropic is involved.
Mathematics asks for slowness
OpenAI said it does not intend to collect the reward money if the issue is resolved. But it will take time to verify his proof. As explained on New Scientist“Demonstrations generated by AI are often difficult to understand and rarely offer the same level of new insights as those created by humans.”
“There has been a very strange and unprecedented disconnect between getting answers and gaining understanding this year,” he told the New Scientist Terence Tao, mathematician at the University of California, Los Angeles. The scientist is referring to the fact that AI is achieving historic results in proving mathematical problems in such a rapid way, that there is no time to fully understand it.
The process of evaluating the new result by the Clay Institute will be slow and rigorous, the same characteristics which, in this chase with posts and press conferences, seem to have been somewhat lost.
