OpenAI claims Navier-Stokes proof amid credit dispute

OpenAI said it has produced an AI-generated solution to the Navier-Stokes equation, a 200-year-old equation describing how fluids like water and air behave, and one of the Clay Millennium Prize problems, each worth $1 million. The announcement was immediately contested: NYU mathematician Tristan Buckmaster says OpenAI rushed its own effort after learning of related work by him and Anthropic researcher Levent Alpöge, and that OpenAI tried to influence how credit for the achievement would be assigned.

Sebastien Bubeck, a mathematician and AI researcher at OpenAI, told a press briefing that the company began training a new AI model with advanced mathematical capabilities on August 28. After hearing rumors that Anthropic was making progress toward Navier-Stokes, OpenAI put more than 1,000 agents on the problem for more than 50 hours, then scaled up to as many as 10,000 agents before the company concluded it had a solution. "I thought there must be a mistake somewhere," Bubeck said. "And on Sunday morning we had the final solution, Lean-formalized and everything." Mark Chen, OpenAI's head of research, said the compute involved cost "in the millions of dollars."

On Monday, Alpöge and Buckmaster posted documents of their own, claiming key advances in a related area they call "unforced Euler." The pair says they used several AI models, including Claude and Codex, to do the work.

Buckmaster then posted a statement saying that, last week, he learned OpenAI had become aware of his and Alpöge's work and had started putting significant resources toward the Navier-Stokes problem. He says he asked OpenAI leaders whether the company had accessed the pair's Codex logs, and was told the model "didn't look up user data," but that OpenAI did not answer his questions about training. He says OpenAI then offered him several "proposals," including one under which he could publish a paper crediting an internal OpenAI model with solving Navier-Stokes without including Alpöge's name.

Bubeck pushed back on social media on the idea that OpenAI had suggested dropping Alpöge's name, and OpenAI CEO Sam Altman also weighed in to defend the team's work. Buckmaster, Alpöge and Anthropic did not immediately respond to Wired's request for comment. At the briefing, Bubeck and other OpenAI executives denied ever inspecting the pair's Codex prompts to inform their own work: "We, whether it's the researchers or the agents, did not see any of their work until it was released publicly last night," Bubeck said. A company blog post on the work was more guarded, stating that "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." Bubeck separately said, "I want to be extremely clear that we recognize the priority of Levent Alpöge and Tristan Buckmaster's work on unforced Euler, and we have nothing but congratulations to them on this monumental achievement that they have made. To be clear, we did not use their prompt or proof to prompt our models or direct our agents." Ven Chandrasekaran, a mathematician at OpenAI, added that the company's solution was significantly different in nature from the one produced by Alpöge and Buckmaster.

The dispute over credit remains unresolved. As AI takes on more of the work of finding mathematical proofs, such fights could become more common.

Key facts

OpenAI says it used AI agents to produce a Lean-formalized proof related to the Navier-Stokes equation, one of the Clay Millennium Prize problems, each worth $1 million.
Per Sebastien Bubeck, OpenAI put more than 1,000 agents on the problem for over 50 hours, scaled up to as many as 10,000 agents, and reached a final solution on a Sunday morning; Mark Chen says the compute cost was in the millions of dollars.
NYU mathematician Tristan Buckmaster alleges OpenAI accelerated its effort after learning, last week, of his and Anthropic researcher Levent Alpöge's related "unforced Euler" work, and that OpenAI offered a proposal letting him publish crediting an internal OpenAI model without naming Alpöge.
Buckmaster says he asked whether OpenAI accessed the pair's Codex logs and was told the model "didn't look up user data," but that OpenAI would not answer his questions about training; OpenAI's own blog post concedes it "cannot rule out" that de-identified usage data helped improve its models.
Bubeck denies suggesting Alpöge's name be dropped and says neither researchers nor agents saw the pair's work before publication; OpenAI mathematician Ven Chandrasekaran says the two solutions differ in nature, and Buckmaster, Alpöge and Anthropic had not responded to Wired's request for comment.

Why it matters

OpenAI is presenting the episode as proof that agentic AI, thousands of instances searching in parallel, can now produce a machine-checked (Lean-formalized) solution to a problem mathematicians had not cracked in two centuries, on one of the Clay Millennium Prize problems. But the same episode shows the friction that comes with it: when multiple labs point large numbers of agents at the same open problem, priority and credit stop being settled by who publishes first and start being contested in public, with one side accusing the other of using knowledge of its unpublished work.

Who it affects

Mathematicians working on open problems now have to reckon with well-resourced AI labs racing them, sometimes on the same specific sub-problem. Anthropic and OpenAI are directly at odds here, with an Anthropic researcher's own work at the center of the dispute. Users of coding assistants like Codex are affected too: Buckmaster's questions about whether his logs were accessed go to how much visibility a lab has into what its own product's users are doing with it.

How to use it

Treat "AI solves a century-old math problem" headlines with the same caution the mathematics community is applying here: a Lean-formalized proof is a real, checkable claim, but priority and credit are a separate question that formal verification does not settle. Readers following the story should watch for a fuller response from Buckmaster, Alpöge and Anthropic, none of which had answered Wired's request for comment at the time of publication.

How solid is it

The proof itself is described as Lean-formalized, which means it can in principle be independently checked line by line, and OpenAI executives gave specifics on the process: the August 28 model training start, the agent counts, the multi-day timeline, and a compute cost in the millions of dollars per Mark Chen. The credit dispute is far less settled: it rests almost entirely on Buckmaster's own account of private conversations with OpenAI, which Bubeck disputes point by point on the question of Alpöge's name, while OpenAI's blog post hedges rather than flatly denies on the question of whether usage data influenced its models.

Risks and caveats

OpenAI's own blog post does not fully rule out that de-identified data from the pair's use of its products helped improve its models, only calling it unlikely, which leaves the data-access question open rather than closed. Buckmaster's allegations, including the offer to credit an internal OpenAI model while omitting Alpöge's name, are one-sided pending a direct response from OpenAI, Alpöge or Anthropic. The article does not say whether OpenAI's Navier-Stokes proof and Alpöge and Buckmaster's unforced Euler work solve the same mathematical problem, only that they are in a related area, and it reports no resolution to the credit dispute.

“I want to be extremely clear that we recognize the priority of Levent Alpöge and Tristan Buckmaster's work on unforced Euler, and we have nothing but congratulations to them on this monumental achievement that they have made. To be clear, we did not use their prompt or proof to prompt our models or direct our agents.”

— Sebastien Bubeck, OpenAI