OpenAI says one of its AI systems has cracked a math problem that has resisted mathematicians for nearly a century, a feat tied to a $1 million prize. Within a day, rival researchers were publicly disputing who actually deserves the credit.
The company announced on September 8 that a model more advanced than its GPT-6 Astra system had proved the three-dimensional Navier-Stokes equations can develop a singularity, a point where a solution effectively blows up, in finite time. Axios reports the announcement came after OpenAI heard rumors that rival teams were closing in on the same result.
According to Quanta Magazine, OpenAI deployed roughly 10,000 autonomous AI agents that worked together for 88 hours, exchanging nearly 5 million messages before producing a proof formally verified using the Lean programming language. The compute bill alone is estimated to have run into the millions of dollars.
The Navier-Stokes equations describe how fluids move, from blood in the human body to air over an aircraft wing to weather systems. Whether their three-dimensional form always produces smooth, well-behaved solutions has been one of seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000. Only one, the Poincare conjecture, had previously been solved. Each remaining problem carries a $1 million award, though OpenAI says it does not intend to claim the money.
A dispute over credit
The announcement landed one day after NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpoge posted their own results on a related problem, the Euler equations. Buckmaster has since questioned whether OpenAI pursued the Navier-Stokes problem only after learning of his team’s work, and whether unpublished material fed into OpenAI’s solution.
Buckmaster said the earliest AI-generated proof he saw from the effort was rough. “I can say the first LLM generated proof Levent sent me was the most horrendous I have ever read,” he said, according to Quanta Magazine.
He has also alleged that OpenAI researcher Sebastien Bubeck pushed to have Alpoge removed from authorship because of his employment at rival lab Anthropic, allegedly warning him, “Why would you ruin your career?”
OpenAI chief executive Sam Altman pushed back on the idea that the two teams’ work overlapped improperly. “Now that we can see their work, the approaches appear to be different,” he said.
Much of the underlying mathematical insight traces back to Diego Cordoba and Luis Martinez-Zoroa, who developed an “infinite cascade” technique for building singular solutions out of smoother ones. OpenAI’s agents adapted that approach to meet the prize’s specific requirements. Princeton mathematician Charles Fefferman, who wrote the official problem description for the Clay Institute, was blunt about where the real breakthrough came from. “The heroes of the story are Cordoba and Martinez-Zoroa,” he said.
Buckmaster went further, arguing Martinez-Zoroa’s underlying contribution deserves the field’s top honor. “In view of this body of work, I believe Luis Martinez-Zoroa deserves a Fields Medal,” he said. For his part, Martinez-Zoroa was gracious about being overtaken in the race to a full proof. “I’m very happy for Tristan,” he said. “It would have been nice to do this ourselves, but I’m very happy for him.”
Why it matters
Disputes over authorship are common in mathematics, but rarely play out this publicly or this fast, a sign of how AI labs are now racing to claim landmark scientific results as proof of their models’ capabilities. The same week, US senators opened a probe into OpenAI’s rogue AI agents, and Wire Examiner reported on a related dispute involving an Anthropic safety researcher’s resignation following a separate AI hacking incident.
For readers in Pakistan, the episode is a reminder of how quickly frontier AI labs are moving into territory once reserved for years of human research, a trend that Pakistani universities and policymakers are only beginning to grapple with as they weigh AI curricula and research partnerships. Institutions such as NUST, LUMS and PIEAS have expanded AI and applied mathematics programs in recent years, and cases like this one, where thousands of AI agents outpace individual researchers on a decades-old problem, are likely to shape how such programs approach AI as a research tool rather than just a subject of study.
Whether OpenAI’s proof holds up to full peer review, and whether it or the Cordoba-Martinez-Zoroa line of work is judged the true origin of the breakthrough, remains to be settled. For now, the Clay Mathematics Institute has not said how or whether it will formally recognize either claim.
