Technology and Science09 September, 20263 min read
OpenAI Says Unreleased Model Solved Navier-Stokes Millennium Prize Singularity Problem
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OpenAI announced an unreleased model solved the Navier-Stokes Millennium Prize problem. Mathematicians raise questions about cheating and intimidation surrounding the breakthrough.
Navier-Stokes Prize Claim
OpenAI said Tuesday that an unreleased artificial intelligence model resolved one of the seven Millennium Prize problems, claiming its internal model proved the three-dimensional Navier–Stokes equations can develop a singularity in finite time.
The claim centers on the Navier-Stokes equations, which mathematicians use to model how fluids move, and the prize is $1 million as one of seven Millennium Prize problems designated at the turn of the century as the most important in the field.
OpenAI said the effort began Sept. 1 after OpenAI researchers heard rumors that two Millennium Prize problems had been solved and launched its new internal model at the remaining problems.
On a call with reporters, OpenAI executives said they devoted enormous computing power to the effort, putting the cost of solving the problem in the "millions of dollars" with roughly 10,000 agents at work.
OpenAI also said it does not intend to claim the $1 million Millennium Prize, framing the result as evidence of how quickly its most advanced systems are improving.
Credit Dispute and Denials
The announcement was overshadowed by questions from NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge about whether OpenAI raced down a direction it learned from their work. Buckmaster said in a statement that "There is another part of this story" and described OpenAI’s parallel effort as involving a tangle of academic rivalries and conflicting claims. OpenAI CEO Sam Altman said, "We were curious if ours could do it too," after admitting OpenAI launched the effort after hearing rumors that Anthropic's models had solved a major math problem.
OpenAI chief research officer Mark Chen told reporters, "No people or AI systems searched through user data to solve this problem," while Buckmaster raised concerns that Codex interactions could have informed OpenAI’s own efforts. In a press briefing on Tuesday, OpenAI mathematician Sébastien Bubeck denied that the two mathematicians’ work had influenced OpenAI, saying, "We did not use their prompt or proofs to prompt our models."
What’s at Stake Next
The dispute is playing out as OpenAI confronts broader questions about how quickly to push the capabilities of its most advanced models, with the company saying on the call that it had "paused a lot" of frontier training after discovering the cyber capabilities of its latest models. Axios reported that the controversy taps into a core trust question for AI-assisted science: whether researchers can safely use frontier labs' tools to work on unpublished discoveries. The stakes also include how credit and verification work in AI-assisted math, with Scientific American noting OpenAI’s proof was certified using the programming language Lean, which all but guarantees its correctness.
Buckmaster’s allegations, as described by TechCrunch, include that OpenAI’s team had become convinced that his and Alpöge’s approach was the right one and decided to reach a formal proof first, after "information about our progress had been passed to OpenAI." OpenAI’s response, as quoted by Axios, emphasized that its researchers and agents did not see Buckmaster and Alpöge’s work before the pair released it publicly, even as the two teams pursued related lines of research rooted in the same earlier work.