OpenAI has claimed an unreleased advanced model has solved one of the most complex problems in mathematics, the Navier–Stokes Millenium Prize problem, in just 88 hours.

In a press briefing, Sebastien Bubeck, mathematician and AI researcher at the company, said that the model had found a solution to the 200 year-old equation attempting to model the natural behaviour of fluids and liquids.

The tool used as many as 10,000 individual agents at one time to find the proof, Bubeck said.

Mark Chen, head of research at OpenAI, added that finding the proof was significantly more expensive than previous mathematical endeavours the company had pursued, requiring spend “in the millions of dollars”.

However, the breakthrough’s provenance has been disputed by New York University mathematician Tristan Buckmaster, who said that the ChatGPT maker intensified its efforts to solve the problem after learning that he was making progress on the problem alongside a researcher at rival Anthropic.

Buckmaster and Anthropic researcher Levent Alpöge posted documents on Monday claiming that they had made key advancements in an area related to the Navier-Stokes problem. The pair also used large language models to complete their work, and said in the announcement that the “far bigger story” was how advanced frontier AI models have become.

Buckmaster has also released a statement claiming that OpenAI only began seriously attempting to solve the Navier-Stokes problem after learning that he and Alpöge were working on a solution.

He claimed that OpenAI reached out to him and offered several proposals for sharing an announcement of the proof, including one in which Buckmaster could publish a paper announcing that the mathematical problem had been solved by an internal OpenAI model, but this would not have included Alpöge’s name.

Buckmaster said in his statement that he had threatened to go public with the conversation if OpenAI attempted to force him to accept one of their proposals, and that someone at the company had responded:“Why would you ruin your career?”

He also claimed that when asked whether data put into the company’s Codex model could have been accessed while pursuing the solution, he was told that the model “didn’t look up user data”, but that it did not answer a follow-up question around the possibility of the model having been trained on his data.

In a statement on its website on Wednesday, OpenAI said that it did not see any of Buckmaster or Alpöge’s work specifically, but that “while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠”. However, it added, its proofs differ substantially from those discovered by Buckmaster and Alpöge.

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