On Tuesday, OpenAI CEO Sam Altman called the breakthrough "one of the most amazing moments" in the company’s history after an internal AI system and 10,000 agents produced a proposed solution to the decades-old Navier-Stokes problem.
OpenAI Says AI Solved Millennium Prize Problem
Altman took to X to highlight OpenAI’s announcement that an internal model, significantly more capable than GPT-6 Astra, had solved the Navier-Stokes existence and smoothness problem.
"One of the most amazing moments for me in OpenAI history was watching this happen over the past week," Altman said.
The problem, unresolved for roughly 90 years, asks whether the equations used to describe fluid motion can develop a mathematical singularity, where a quantity becomes unbounded in finite time.
OpenAI said about 10,000 AI agents worked together for 88 hours to produce the result.
If it withstands scrutiny, it would be the most significant mathematical proof produced by AI to date, potentially transforming how mathematicians tackle complex problems.
AI Agents Produced Proof Checked With Lean
According to OpenAI, the agents produced an analytical proof showing that three-dimensional Navier-Stokes dynamics can develop a singularity.
The result was subsequently formalized in Lean, a computer-assisted system used to verify mathematical proofs.
The Navier-Stokes problem is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute, with each carrying a $1 million prize.
Anthropic Work Raises Questions Over OpenAI’s Breakthrough
The breakthrough also comes amid questions over closely related research by NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge, who had been investigating similar fluid-dynamics problems.
In the blog post, OpenAI said its work began Sept. 1 after researchers heard a rumor involving Alpöge and Tristan Buckmaster. After completing its project and verifying the proof in Lean on Sept. 6, OpenAI contacted the researchers, believing they had solved the Navier-Stokes problem as well.
The company proposed a joint announcement but later learned their breakthrough involved the related forced Euler problem. OpenAI said it offered Alpöge and Buckmaster access to the prompts used in its project and later offered to share its proof.
"We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement," OpenAI said.
The company also said its researchers and AI agents did not access the pair’s work before it was made public and that "no specific user data was accessed" to solve the problem.
OpenAI acknowledged it could not completely rule out whether anonymized user data may have helped improve its models, but said its proof differed significantly from the researchers’ work.
Altman also defended the company, saying, “We would have greatly preferred coordination. We did not rush to publish even though the other team wasn’t communicating with us. The team threatened us with unfounded accusations of plagiarism.”
Disclaimer: This content was partially produced with the help of AI tools and was reviewed and published by Benzinga editors.
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