OpenAI Says It Found an AI Solution to the Navier-Stokes Equation, Drawing Dispute Over Credit

OpenAI announced it has found an AI-generated solution to the Navier-Stokes equation, a 200-year-old problem tied to the behavior of fluids like water and air. The claim is now entangled in a dispute over whether the company accelerated its work after learning of progress by other researchers.

Navier-Stokes and the Clay Millennium Prize

The proof relates to the Navier-Stokes equation, one of the unsolved problems in the Clay Millennium prizes, each worth $1 million. OpenAI said it used a Lean-formalized proof, with Sebastien Bubeck describing a final solution reached on Sunday morning.

OpenAI’s training timeline and compute costs

Sebastien Bubeck said OpenAI began training a new AI model with advanced mathematical capabilities on August 28. After reading rumors that Anthropic was making progress on Navier-Stokes, OpenAI dedicated more resources to the problem, deploying more than 1,000 agents over more than 50 hours.

Mark Chen, head of research at OpenAI, said the effort required substantially more computing power than prior math work, costing “in the millions of dollars.”

Competing claims from NYU and Anthropic researchers

On Monday, Tristan Buckmaster of NYU and Levent Alpöge of Anthropic posted documents describing advances in an area relevant to Navier-Stokes. Their work used several AI models, including Claude and Codex.

Buckmaster also posted a statement claiming he learned last week that OpenAI had become aware of his and Alpöge’s progress and had started dedicating significant resources. He said he asked OpenAI leaders whether the company accessed his and Alpöge’s Codex logs, and that he was told the model “didn’t look up user data.” He added that OpenAI did not respond to questions about training. Buckmaster said OpenAI offered proposals that included a version where he could publish a paper announcing Navier-Stokes was solved by an internal OpenAI model without Alpöge’s name included.

OpenAI denies using private prompts or proofs

In a briefing, Bubeck and other OpenAI executives denied inspecting the pair’s Codex prompts to inform their work. Bubeck said OpenAI’s team did not see the other researchers’ work until it was released publicly “last night,” and he said OpenAI recognizes the priority of Alpöge and Buckmaster.

Ven Chandrasekaran, a mathematician at OpenAI, said OpenAI’s solution is different in nature from the one produced by the other researchers.

Why this matters

Navier-Stokes is among the most prominent open problems in mathematics, and the dispute shows how quickly credit and access questions can surface as AI systems take on proof work. The outcome may shape how researchers and institutions handle attribution as computational methods become more central to scientific discovery.