OpenAI has claimed a major breakthrough in mathematics after an unreleased artificial intelligence model produced what the company describes as a solution to the Navier-Stokes problem in just 88 hours.
The company said the effort involved about 10,000 AI agents working together and millions of dollars in computing resources.
The Navier-Stokes problem is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1m prize for an accepted solution.
OpenAI said its internal model produced an analytical proof and a formalised version in Lean, a computer-based proof assistant. According to the company, the work demonstrates that the equations governing fluid motion can develop a singularity in finite time.
The Navier-Stokes equations are used to describe the movement of fluids such as air and water. They underpin mathematical attempts to understand phenomena ranging from turbulence and weather systems to airflow and other fluid behaviour.
The central mathematical question is whether smooth three-dimensional solutions always exist and remain well behaved, or whether they can break down.
OpenAI said the result was generated by a next-generation model that is significantly more capable than GPT-6 Astra, its current publicly identified frontier model.
The company said the project began on September 1 after researchers heard rumours concerning mathematical work by New York University mathematician Tristan Buckmaster and Levent Alpöge, an Anthropic researcher.
OpenAI subsequently directed its internal system at the Navier-Stokes problem and other remaining Millennium Prize Problems.
According to the company, the system eventually produced the claimed Navier-Stokes solution after 88 hours, with about 10,000 agents coordinating their work.
The breakthrough has not, however, been officially recognised as a solution to the Millennium Prize Problem.
Under the Clay Mathematics Institute’s rules, a proposed solution must be published in a qualifying outlet, undergo rigorous examination for at least two years and receive general acceptance in the global mathematics community before it can be considered for the prize.
That means the mathematical community will now have to examine OpenAI’s proof independently.
The announcement has also triggered a dispute over research credit.
Buckmaster and Alpöge recently published AI-assisted work concerning several related fluid equations. Their research demonstrated finite-time breakdowns in related systems and used computer-assisted verification.
Buckmaster subsequently questioned the timing of OpenAI’s work and suggested that the company’s researchers had pursued an approach similar to one developed by him and Alpöge.
OpenAI has denied accessing the pair’s unpublished research or using their prompts and proofs to direct its AI agents.
The company later acknowledged that, while it considered the possibility unlikely, it could not rule out de-identified data from users of its products having contributed to the training of its models.
The dispute adds another dimension to the growing debate over AI-assisted scientific research, particularly the questions of intellectual property, authorship and how much credit should go to humans when artificial intelligence generates mathematical discoveries.
For now, OpenAI’s achievement should be described as a claimed solution, rather than a formally accepted resolution of the Navier-Stokes problem.
If independently verified, however, it would represent one of the most significant demonstrations yet of artificial intelligence being used to tackle a longstanding problem at the frontier of mathematics.
