OpenAI Says AI Cracked a 200-Year-Old Maths Problem. Another Mathematician Says the Company Raced Ahead After Learning of His Work.

Key points

• OpenAI announced on a Monday in 2025 that an AI model had produced a formal proof for the Navier-Stokes equation, a 200-year-old maths problem worth a $1 million Clay Millennium Prize.
• The company spent "millions of dollars" in computing costs and ran over 1,000 AI agents for more than 50 hours to reach the result.
• Mathematician Tristan Buckmaster of NYU alleges OpenAI learned of his and co-author Levent Alpöge's parallel progress before racing to publish its own solution.
• OpenAI denies accessing the pair's private work and says it recognised their prior contribution publicly.
• The dispute raises a question that will recur: when AI does the heavy lifting on a discovery, who gets the credit?

For two centuries, one equation has defeated the greatest mathematical minds on Earth.

The Navier-Stokes equation describes how fluids, like water and air, flow and swirl. Solving it completely, meaning producing a formal proof that the maths holds under all conditions, is one of seven Millennium Prize Problems set by the Clay Mathematics Institute, each carrying a $1 million reward. No one has done it. Until, OpenAI claims, now.

What exactly did OpenAI do?

OpenAI says an AI model it began training on 28 August produced a complete, verified proof. The company directed more than a thousand AI agents, software programs that can carry out long chains of reasoning on their own, at the problem. They ran for over 50 hours before landing on a solution.

Sebastien Bubeck, a mathematician and AI researcher at OpenAI, told a press briefing he initially assumed the result was wrong. "I thought there must be a mistake somewhere," he said. "And on Sunday morning we had the final solution, Lean-formalized, and everything." Lean is a programming language used to write out mathematical proofs in a form a computer can check step by step.

Mark Chen, OpenAI's head of research, confirmed the computing time alone cost "in the millions of dollars."

Why are other mathematicians unhappy?

On the same Monday OpenAI made its announcement, Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic, the AI company, posted their own documents showing significant advances on a closely related part of the Navier-Stokes problem. They used several AI models, including Claude and Codex (an OpenAI coding tool), in their work.

Buckmaster then posted a separate statement with a serious allegation. He says he learned last week that OpenAI had become aware of his and Alpöge's progress, and had begun pouring resources into the problem. He claims he asked OpenAI leaders whether the company had looked at the pair's Codex usage logs, private records of the questions they had typed into the tool. He says he was told the model "didn't look up user data," but that OpenAI did not answer questions about whether their data had been used in training.

Buckmaster also claims OpenAI offered him a deal: he could publish a paper announcing the solution as the work of an internal OpenAI model, but without Alpöge's name on it.

OpenAI flatly denies both accusations. "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. The company says it recognises Buckmaster and Alpöge's contribution to a related part of the problem and stresses that its own solution followed a significantly different path.

Wired AI, which first reported the full exchange of claims, noted that Buckmaster, Alpöge, and Anthropic did not respond to requests for comment before publication.

What does this mean for science?

For patients and the public, a proof of Navier-Stokes has long-term implications for how we model weather, design aircraft, and understand blood flow in the body. Those applications are years away from any practical change.

The immediate question is simpler and sharper. As AI takes on more of the intellectual labour in research, credit disputes like this one will become harder to settle. Who owns a discovery when the thinking was done by software, the software was built by one company, and the direction came from researchers at another?

That question has no clean answer yet.

Common questions

Does this mean the Navier-Stokes prize money has been awarded?

Not yet. The Clay Mathematics Institute has its own formal review process, and no prize has been announced. Independent mathematicians will need to verify the proof before any award is considered.

Could AI have cheated by reading private research notes?

OpenAI says no, and denies accessing any private Codex logs. Buckmaster disputes this. The full facts are not yet established, and the story is still developing.

What is the Navier-Stokes equation and why does it matter?

It is a set of mathematical rules, written down in the early 1800s, that describe how liquids and gases move. Fully solving it would sharpen everything from hurricane forecasting to the design of more efficient engines and medical devices.