OpenAI says it has found a solution to a major mathematics problem that had remained unsolved for around 90 years. In a blog post published on Tuesday, the company announced that it had discovered a solution to the Navier-Stokes problem, which relates to the flow of liquid and gas, using an internal AI model described as more powerful than the newly released GPT-6 Astra, working alongside 10,000 concurrent agents.
The Navier-Stokes problem is one of seven Millennium Prize Problems, each carrying a reward of roughly £790,000 for a verified solution. OpenAI says it began training the internal model on 28 August, and that the system has shown unprecedented performance across its benchmarks, including mathematics. The company has stated that it does not plan to claim the prize money.
A breakthrough shadowed by controversy
The announcement did not arrive without dispute. Just one day earlier, New York University mathematics professor Tristan Buckmaster published findings on a related problem in partnership with Levent Alpöge, a researcher at Anthropic. When presenting the results, Buckmaster said he had contacted OpenAI after learning the company had heard about their progress.
Buckmaster subsequently found that OpenAI had produced a proof for the Navier-Stokes equation using a route he and Alpöge had been developing with OpenAI’s Codex and Anthropic’s Claude. In his statement, he raised concerns about whether OpenAI had accessed their Codex data to move closer to a solution.
“I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” Buckmaster wrote. “I was told the model did not look up user data. I asked again, about training, and I did not get an answer.”
OpenAI responds to data concerns
OpenAI has sought to address these suspicions with its Tuesday statement, saying that no specific user data was accessed in order to solve the problem. It added that, while unlikely, it could not rule out that de-identified data derived from the pair’s use of its products may have helped improve its models.
Sebastien Bubeck, a member of technical staff at OpenAI, said the company had not seen any of Buckmaster and Alpöge’s work until it was released publicly the previous night. He added that the proofs differ significantly and that even the precise results proved are different.
Buckmaster responded in a post on Mastodon, claiming that OpenAI was openly admitting it had used training data from a period after he and Alpöge found their result. OpenAI has said it does not plan to take the £790,000 prize.
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Image: theverge.com
