OpenAI said Tuesday that one of its unreleased artificial intelligence models had solved the Navier-Stokes problem, one of the world’s most difficult mathematical puzzles, after just 88 hours of work involving 10,000 AI agents and millions of dollars in computing power.
The claim concerns one of the seven Millennium Prize Problems established by the Clay Mathematics Institute, a collection of mathematical questions that have challenged researchers for generations.
Navier-Stokes concerns equations describing how fluids such as air and water move, with applications ranging from aircraft design and weather forecasting to the study of blood flow.
OpenAI researchers said their work showed that the equations can break down over time, answering the question posed by the Millennium Prize.
This is a significant milestone for AI research, and its promise for the world is that even more of our hardest questions would become possible to answer,” Mark Chen, OpenAI’s chief research officer, told reporters.
Each Millennium Prize Problem carries a $1 million reward, although OpenAI said it would not seek the prize if its finding is eventually confirmed.
The claim is not yet an accepted mathematical solution.
Under the prize rules, a proposed solution must first be published in a peer-reviewed journal and then survive two years after acceptance within the mathematical community before the institute will convene a committee to consider the work.
“The process of evaluation is deliberately unhurried, and we shall ensure that it is absolutely rigorous,” Professor Martin Bridson, president of the Clay Mathematics Institute, told AFP.
OpenAI said it began training the new model in late August, describing it as more capable than anything it had previously released publicly.
Days later, after seeing online rumours that a competitor had solved Millennium problems, the company said it directed the system at all six remaining unsolved problems.
The Navier-Stokes problem soon showed promise, prompting OpenAI to commit substantial computing resources to the effort.
By the final stage, OpenAI researcher Sebastien Bubeck said, 10,000 AI agents were working on the problem simultaneously and communicating with one another.
Chen said the computing costs ran “emphatically in the millions of dollars,” while Bubeck said this was roughly 1,000 times what the company had spent on earlier mathematical results.
According to OpenAI’s account, the AI agents reached a solution on Saturday, about 88 hours after the project began.
The claim also triggered a dispute over credit with rival researchers.
Hours before OpenAI announced its result, Tristan Buckmaster, a mathematician at New York University, and Levent Alpoge, who works at OpenAI rival Anthropic, released AI-assisted work on three related equations.
In a statement published alongside his papers, Buckmaster said OpenAI had taken up the problem only after information about his research spread and had pursued the same unusual approach that he and Alpoge had spent months developing.
OpenAI researchers denied accessing the rival team’s work.
“To be clear, we did not use their prompts or proofs to prompt our models or direct our agents,” Bubeck said.
OpenAI later acknowledged on X that “while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
The episode has added to a growing debate over the role of artificial intelligence in advanced mathematics and whether machine-generated solutions should be regarded as demonstrating genuine mathematical understanding.
For now, the Clay Mathematics Institute says the claimed breakthrough will face the same rigorous evaluation required of any proposed solution to a Millennium Prize Problem.
AFP
