# When A.I. Solved a Million-Dollar Math Problem, Questions of Credit Followed
In September 2026, OpenAI announced that an internal system had solved the Navier-Stokes problem, a mathematical puzzle concerning fluid movement that has challenged researchers for nearly two centuries. The achievement required approximately 10,000 artificial intelligence agents working largely autonomously for 88 hours, using computational power that likely cost millions of dollars. Yet the announcement immediately sparked questions about whether human mathematicians' work had contributed to the breakthrough.
The Navier-Stokes problem traces back to equations written by Claude-Louis Navier and George Gabriel Stokes to describe how fluids move. Mathematicians have since investigated whether these equations work in all situations or whether they allow for a theoretical case in which a small part of the fluid moves infinitely quickly and the solution breaks down—what researchers call a "blowup." The problem is fundamentally a yes or no question: one must either prove that the equations always result in smooth solutions or find one specific situation where they don't.
OpenAI claims to have found one such blowup scenario, involving a vortex of fluid that spirals inward and becomes stretched out, like spaghetti. The company verified its A.I. agents' work using a programming language called Lean. The Navier-Stokes existence and smoothness problem is one of seven Millennium Prize Problems designated by the Clay Mathematics Institute, each carrying a one million dollar reward.
The controversy emerged because two human scientists were also working on the Navier-Stokes problem when OpenAI instructed its agents to find a solution. OpenAI wrote in its blog post that it was inspired to address the open Millennium Prize problems after hearing rumors that two of them had been solved. The company began work on September 1, later realizing that the rumors regarded Anthropic mathematician Levent Alpöge and New York University mathematician Tristan Buckmaster.
In a statement, Buckmaster wrote that he and Alpöge had made significant progress on the Navier-Stokes problem but had not yet published their work. He explained that they used large language models, including OpenAI's Codex. In a conversation with OpenAI employees, Buckmaster asked whether the model had been trained on or had access to their sessions in Codex, into which they had been putting all their drafts for the project. "I was told the model did not look up user data," Buckmaster wrote. "I asked again, about training, and I did not get an answer."
"I do not know whether our data was used," Buckmaster added. "I am not accusing anyone of anything."
OpenAI maintains that its researchers and A.I. agents didn't see Buckmaster and Alpöge's work until it was released to the public, and that no specific user data was accessed to solve the problem. However, in the blog post, the company also wrote that "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." On Wednesday evening, the company offered a more strongly worded statement: "We can say categorically that it is impossible for Dr. Buckmaster's Codex prompts over the last two months to have influenced the system in any way, including training."
Buckmaster attributes much of his success to the earlier work of Diego Córdoba and Luis Martínez-Zoroa, who had taken steps toward "blowing up" the problem. He and Alpöge used large language models to build on the pair's ideas. "In view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal," Buckmaster wrote.
OpenAI, according to its post, will not be claiming the one million dollar Millennium Prize. Who or what will ultimately get credit for the winning Navier-Stokes solution remains uncertain.
**Sources:**
Smithsonian Magazine. "A.I. May Have Solved a Longstanding Math Problem With a Million-Dollar Prize. It Ignited a Controversy Over Who Gets Credit." September 10, 2026. https://www.smithsonianmag.com/smart-news/ai-may-have-solved-a-longstanding-math-problem-with-a-million-dollar-prize-it-ignited-a-controversy-over-who-gets-credit-180989472/