“We did not use their prompt or proofs to prompt our models,” Sébastien Bubeck, an OpenAI mathematician, said at a press briefing on Tuesday, as the company defended its claim to have solved part of one of mathematics’ most difficult outstanding problems.
OpenAI said on Tuesday that a new artificial intelligence model, working through roughly 10,000 AI agents, had found a solution to part of the Navier-Stokes problem in 88 hours. The equations describe how fluids move, and important aspects of them have lacked a proof for 90 years. The company’s result has yet to undergo independent verification or gain public acceptance from the Clay Mathematics Institute.
The claim would be a striking demonstration of AI’s ability to work through advanced mathematics. It has also become a test of OpenAI’s standing with academic researchers after Tristan Buckmaster, a mathematics professor at New York University, accused the company of beginning its work only after information about his and Levent Alpöge’s progress had reached it.
The Navier-Stokes existence and smoothness problem is among the seven Millennium Prize Problems selected by the Clay Mathematics Institute in the year 2000. The institute offers a $1 million prize for the first correct solution to each challenge.
OpenAI said it heard rumours on 1 September that two Millennium Prize problems had been resolved. By 5 September, after setting its 10,000 AI bots to work, it said it had reached a solution to the Navier-Stokes existence and smoothness problem. The agents exchanged nearly 3 million messages and generated 130 billion output tokens on Navier-Stokes alone.
The result resolved two of the four statements required by the Millennium Prize proof. OpenAI said, “We do not intend to claim the Millennium Prize for this result”.
Buckmaster said on Tuesday that he and Alpöge had been working towards solutions to the problem. He said information about his progress had been passed to OpenAI. Buckmaster claimed that OpenAI began work on the Navier-Stokes equations after that information reached the company.
Buckmaster and Alpöge released competing proofs using artificial intelligence models from Anthropic and OpenAI. OpenAI’s approach to the full Navier-Stokes problem followed a similar method to the one used by the two mathematicians, according to the account of the competing work.
OpenAI rejects the allegation that it had improper access to the academics’ research. Bubeck said the company had not used the pair’s prompts or proofs to direct its models.
The dispute leaves several questions unresolved. It remains unclear how information about Buckmaster and Alpöge’s progress reached OpenAI after the company heard rumours on 1 September, or whether the two approaches were independently developed. External mathematicians have yet to assess the full technical case for OpenAI’s proof, and the Clay Mathematics Institute has yet to decide whether it will recognise the company’s partial result.
For OpenAI, the issue extends beyond a single proof. The company has presented the work as a major use of AI agents in mathematical research, supported by substantial computing resources. Its account now rests alongside the academics’ allegation that the effort was prompted by knowledge of their work, an accusation OpenAI firmly denies.
Comments (0)