Most of the world has marveled at how an AI solved a Millennium problem, but top mathematicians don’t seem to be sharing the enthusiasm.
Cédric Villani, the French mathematician and Fields Medal winner, says OpenAI’s claimed solution to the Navier-Stokes problem has left him rattled. He was awarded the Fields Medal in 2010, and he was the director of Sorbonne University’s Institut Henri Poincaré from 2009 to 2017. As of September 2025, he is a professor at the École normale supérieure de Rennes.
“I was shaken. An atmosphere of the end of history,” Villani said, according to a French press report on how mathematicians are reacting to the result. “It’s a cataclysm unlike anything mathematics has ever known.”
What OpenAI claimed #
On September 8, OpenAI announced that about 10,000 autonomous AI agents running on an unreleased model had found a singularity in the three-dimensional Navier-Stokes equations, resolving one of the seven Millennium Prize Problems. The agents reached their result about 88 hours after they were first launched. OpenAI also published a Lean formalization so the proof can be machine-checked. The result also arrived amid a credit dispute with mathematicians Tristan Buckmaster and Levent Alpöge which saw the researchers sparring on X.
A sharp turn from Villani’s earlier position #
Villani’s reaction has drawn attention because of how skeptical he has been of AI. Just last month he argued that large language models are not intelligent and understand nothing of what they say. He offered as proof that these models get the “car wash” example wrong, and that he has made much the same argument for years.
In a 2024 conference, Villani had reportedly described AI systems as “just functions f(x)=y,” and therefore “no smarter than the formula that calculates your taxes.” The contrast with his current alarm is what’s getting eyeballs on X.
Villani isn’t alone #
Other mathematicians too have expressed skepticism about the pace at which AI is able to churn out proofs to problems that mathematicians have spent decades working on. Last week, 25 Fields medal winners had signed a letter saying that rapid AI proofs were harming mathematics in a “severe misalignment”. The declaration argued that AI companies, chasing benchmarks and headlines, are turning problem-solving into a “mass production” of true/false statements that displaces this process rather than feeding it. Separately, OpenAI had to drop its sponsorship of a college mathathon after opposition from mathematicians.
What comes next #
The proof is still being checked by the wider community. OpenAI has also said it has made substantial progress on another Millennium Prize problem since finishing Navier-Stokes, and is working out how to share those results thoughtfully. If that claim holds up, the mathematicians now describing a cataclysm may have more to react to soon.