On Tuesday, NYU mathematics professor Tristan Buckmaster announced three proofs, including a preliminary finding on one of the most storied unsolved problems in theoretical mathematics. The work, conducted with Anthropic mathematician Levent Alpöge and leveraging both Codex and Claude AI models, is significant in its own right. But it has also ignited an unusual controversy concerning OpenAI's parallel efforts to solve the same problem.
“There is another part of this story,” Buckmaster wrote in his [statement](https://cims.nyu.edu/~tristanb/statement.pdf) announcing the proofs, “and one that, honestly, I very much wish I did not have to be concerned with.”
While Buckmaster and Alpöge were finalizing their results, they learned that “information about our progress had been passed to OpenAI.” When they contacted the company, OpenAI claimed it had already achieved a complete proof of the central problem. But when pressed on when its research began and how much human guidance was involved, Buckmaster says the responses became evasive.
“It emerged that an entire team had been working on the problem,” Buckmaster explained, “and that an insane amount of compute had been used… Eventually, it was agreed that [the first prompt] had been sent in the past few days, after information about our work had reached OpenAI.”
If accurate, that sequence suggests OpenAI, convinced that Buckmaster and Alpöge were on the right track, marshaled its massive computational resources to reach a formal proof first.
Sebastian Bubeck, who leads OpenAI's mathematical research, rejects the claims as “false and inflammatory.” In a post responding to Buckmaster's statement, Bubeck wrote: “To clarify, I came into the discussion following academic norms, and I'm disappointed that it has come to this. Anyone who knows me knows that academic standards are of the highest importance to me.” He has pledged to issue a fuller statement in the near future.
At the heart of the dispute is the Navier–Stokes existence and smoothness problem—one of the seven [Millennium Prize Problems](https://www.claymath.org/millennium-problems/), each carrying a $1 million bounty from the Clay Mathematics Institute for a verified solution. The Navier–Stokes equations, central to fluid mechanics, remain poorly understood from a theoretical standpoint. A solution would mark a major advance in mathematical physics.
While the problem attracts widespread attention, the specific route Buckmaster and his collaborator took is far less common. That, Buckmaster says, is what made OpenAI's apparent convergence on the same approach at the same time so suspicious.
“The route to the Clay problem through a smooth force, options c and d in Fefferman's statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack,” he wrote. “Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement.”
Notably, Alpöge's work was independent of his employer Anthropic, and the duo used a mix of AI models—including Anthropic's Claude and OpenAI's Codex—for their research. The incident raises fresh questions about research ethics and transparency among AI labs competing on high-stakes mathematical problems, especially as AI models become increasingly central to scientific discovery. As of 2026, no official adjudication has been made on the rivalry, and the mathematical community continues to watch how these powerful tools are deployed—and how credit is assigned—in the race for breakthroughs.
via TechCrunch AI