WASHINGTON: OpenAI has claimed that an unreleased artificial intelligence model has solved the Navier-Stokes problem, one of seven Millennium Prize Problems identified by the Clay Mathematics Institute as major unresolved questions in mathematics.
OpenAI said its model reached a proposed solution after about 88 hours of work involving thousands of AI agents and computing resources costing millions of dollars.
The claim has not been independently verified or formally accepted by the mathematical community.
The Navier-Stokes problem concerns equations used to describe the movement of fluids such as air and water. The equations have applications in areas including aircraft design, weather forecasting and blood-flow research.
OpenAI said its research indicates that solutions to the equations can develop breakdowns over time, addressing the central question posed by the Millennium Prize challenge.
Each of the seven Millennium Prize Problems carries a $1 million prize. Only one of the seven problems has been officially solved since the list was established in 2000.
How will OpenAI’s claim be verified?
Under the Clay Mathematics Institute’s rules, a proposed solution must first be published in a peer-reviewed journal and accepted by the mathematical community. It must then remain accepted for two years before the institute considers appointing a committee to evaluate it for the prize.
Clay Mathematics Institute President Martin Bridson said the evaluation process would be rigorous and deliberately lengthy.
OpenAI said it would not seek the $1 million prize if its result is eventually confirmed.
The announcement has also prompted a dispute over the development of the approach used in the claimed solution.
New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpoge had released AI-assisted research on three related equations shortly before OpenAI announced its result.
Buckmaster said OpenAI pursued an approach similar to work that he and Alpoge had been developing for months.
OpenAI researchers denied using their prompts or proofs to direct the company’s AI system. OpenAI later acknowledged that it could not completely rule out the possibility that de-identified data derived from use of its products had contributed to improvements in its models.
How did the AI system tackle the mathematics problem?
OpenAI said it began training a new model in late August and subsequently directed it to examine the six Millennium Prize Problems that remain unsolved.
According to researcher Sebastien Bubeck, about 10,000 AI agents were eventually involved in the Navier-Stokes work, communicating with one another during the process.
OpenAI said the computing costs reached millions of dollars, with the company estimating that the effort cost roughly 1,000 times more than some of its earlier mathematical research.
The claimed result now faces scrutiny from mathematicians. Until the proposed proof is independently examined, published and accepted under the Clay Institute’s rules, the Navier-Stokes problem remains officially unresolved.