OpenAI announced on Tuesday, September 8, that a swarm of 10,000 AI agents produced a solution to the Navier-Stokes Millennium Problem, a result that landed with a thud in a mathematics community already angry about how the company got there.
The announcement capped a five-day sequence that began the previous Thursday, September 3, when NYU mathematician Tristan Buckmaster reached out to a mathematician at OpenAI. Buckmaster wanted the company to know that rumors then swirling about Anthropic having solved two Millennium Problems most likely referred to his own effort, work done in his spare time with Levent Alpöge, an Anthropic employee, and not officially supported by the AI company.
By Sunday, September 6, Buckmaster was speaking with the OpenAI mathematician and Sébastien Bubeck, the OpenAI mathematician who led the company's push on the Millennium Problems. Bubeck offered to merge the two efforts and let Buckmaster write a paper announcing the full Navier-Stokes result, provided the paper acknowledged that an OpenAI model had solved it. Under that offer, Alpöge would not be a co-author.
Buckmaster was furious. On Monday, September 7, he released a statement excoriating OpenAI along with rough drafts of three papers totaling about 245 pages. The next day, OpenAI went public with its swarm.
The company said its approach to Navier-Stokes used the same broad approach as the one Alpöge and Buckmaster had taken, an approach Buckmaster said "almost nobody" was working on. OpenAI began its work only after rumors about an Anthropic effort reached the company.
What the solution actually says
The Navier-Stokes equations describe how a fluid moves through space. Fluid dynamics is complicated enough that in most cases there is no explicit formula for where the fluid will be at every point in the future. The equations instead describe how the fluid's motion is changing by calculating direction and speed at each point in time. To model movement over time, scientists move forward in small steps, using the equations to estimate changes in the velocity field.
The theoretical question at the heart of the Millennium Problem is whether there are situations where the fluid movement predicted by Navier-Stokes leads to absurd outcomes. OpenAI found a fluid arrangement in 3D where the equations do exactly that, producing a singularity in a scenario with a specially chosen smooth force. The company described the result this way: "The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics." In the central region, "the velocity of the fluid grows without bound." That would never happen in a real fluid.
Alpöge and Buckmaster found a similarly implausible outcome for three related and somewhat simpler models of how liquids flow. A simpler model of fluid motion breaks down when a wave turns into a sharp discontinuity, with particles needing to teleport. Their three problems are closely related to Navier-Stokes but not identical to it.
OpenAI's solution is hard to draw, and the company spent millions of dollars on compute to get it.
The fight over credit and norms
The drama overshadowed the mathematics. Observers debated whether Buckmaster was right to be outraged or whether Bubeck's response exonerated OpenAI. Buckmaster's own framing of the episode, released before OpenAI's announcement, was blunt: "I had planned to say on announcing our work that the results are not the important thing. Rather the important thing is instead the significance that a mathematician and an LLM model can now do all this work in a month," he wrote. "instead of these incredibly important developments, I find myself writing about something else."
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Some of OpenAI's behavior might have been reasonable in the context of competing with another well-resourced company like Anthropic. But spending millions of dollars on compute and scooping an academic researcher breaks the norms of the academic math community. Mathematics relies on a community of experts openly sharing ideas. Mathematicians value openness and collaboration, and it is considered bad form to learn of another mathematician's promising early results and then sprint to complete the work first.
If everyone behaved like OpenAI, mathematicians would have to keep their work secret until ready for publication. OpenAI sought to gain prestige by solving a famous math problem, and the way it went about it has arguably undermined the community that made solving the problem prestigious in the first place.
The pattern has precedent. IBM's Deep Blue defeated world chess champion Garry Kasparov in 1997, and AlexNet won the ImageNet competition in 2012. Both moments rearranged how the public thought about machine capability, and both arrived with their own arguments about what had actually been demonstrated.
Tao: intellectually interesting, not transformative
Terence Tao wrote a Mastodon thread on September 3 about the implications of an AI model solving Navier-Stokes, the same day Buckmaster first contacted OpenAI. Tao stated that the regularity problem is not important for direct physical application. He noted that computational fluid dynamics is already a mature subject, deployed extensively in the atmospheric sciences, and that its empirical capabilities and limitations are already well understood.
"A theoretical guarantee of regularity, or conversely a pathological instance of blowup, for these equations would be intellectually interesting for such applications, but would not radically transform the way we would, for instance, model weather prediction or climate change," Tao wrote. In other words, the solution probably will not have much practical significance. The problem is important but useless for practical applications, at least in the near term.
A community problem, not just a company problem
Focusing on the details of the drama risks missing the larger point about the importance of community in mathematics. The question is not only whether OpenAI's result is correct, or whether Bubeck's offer was generous or insulting, but what happens to a field whose members stop sharing early results because a well-funded lab might finish the job first.
Anthropic, for its part, was rumored to have solved two Millennium Problems. Alpöge worked on the project in his spare time, and the effort was not officially supported by his employer. That distinction mattered to Buckmaster, who wanted OpenAI to understand that the rumors pointed at him and Alpöge, not at a corporate research program.
The article covering these events is dated Sep 10, 2026, and is marked as Paid. As of publication it had drawn 142 likes, 2 comments, and 11 shares.