OpenAI says an internal model more powerful than the newly released GPT-6 Astra, running alongside 10,000 concurrent agents, produced a solution to the Navier-Stokes problem — a 90-year-old question about the flow of liquids and gases that sits among the seven Millennium Prize Problems. Each of those problems carries a $1 million reward. OpenAI announced the result in a Tuesday blog post and says it will not claim the prize.
The company began training the internal model on August 28th and says it has "exhibited unprecedented performance in our benchmarks, including mathematics." The proof lands as the biggest single mathematical claim any frontier lab has made, and the first to target a Millennium Prize problem directly.
One day before OpenAI's announcement, New York University mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published findings on a related Navier-Stokes result. The two had been working on their proof using OpenAI's Codex and Anthropic's Claude, uploading drafts into Codex sessions throughout the project. Buckmaster says he contacted OpenAI after learning the lab had heard about their progress, then discovered OpenAI had produced its own proof along a route the two had been pursuing.
Key facts
- 01OpenAI says an internal model more capable than GPT-6 Astra solved the Navier-Stokes problem using 10,000 concurrent agents.
- 02The Navier-Stokes problem is one of seven Millennium Prize Problems, each carrying a $1M reward; OpenAI says it will not claim the money.
- 03OpenAI began training the internal model on August 28th, one day before rival researchers Tristan Buckmaster and Levent Alpöge published a related proof.
- 04Buckmaster, an NYU professor, alleges OpenAI may have trained on his Codex sessions containing drafts of the work.
- 05OpenAI says no specific user data was accessed but concedes de-identified data derived from product usage may have improved the model.
Buckmaster's public statement raises the question directly.
OpenAI's Tuesday post pushes back on the implication. The company says "no specific user data was accessed in order to solve this problem," while adding that "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." That second sentence is the crux of the dispute — a formal acknowledgment that training pipelines may absorb material that individual users would consider their own.
Sebastien Bubeck, a member of OpenAI's technical staff, offered a more direct defense.
“We did not see any of their [Buckmaster and Alpöge's] work until they released it publicly last night. One can in hindsight see that our proofs differ significantly and even the precise results proved are different.”— Sebastien Bubeck, Member of technical staff, OpenAI
Buckmaster responded on Mastodon, arguing that OpenAI is "openly admitting they used training data from a period after we found our result." The timing is what makes the dispute hard to resolve cleanly: the internal model's August 28th training start sits inside the window during which Buckmaster and Alpöge were actively drafting inside Codex, and OpenAI's own carve-out language leaves room for their material to have influenced the model without the lab intending to look at it.
The underlying mathematics matter. The full Navier-Stokes existence and smoothness problem asks whether smooth solutions always exist in three dimensions — a question that has resisted mathematicians since the 1930s. A verified proof would be the first Millennium Prize problem solved since Grigori Perelman's Poincaré conjecture work in the early 2000s, and the first ever produced primarily by an AI system. Peer review has not begun. Bubeck's note that the two proofs "differ significantly" and cover different precise results is the kind of claim the mathematics community will spend months checking.
Independent verification is the only thing that will settle whether OpenAI's proof holds up on its own terms, and whether it stands apart from the Buckmaster-Alpöge work in the way Bubeck describes. Until then, the dispute is a stress test for how frontier labs handle the boundary between what users paste into a product and what ends up shaping the next model. OpenAI's disclosure that de-identified usage data may have helped is unusually candid — and it is also exactly the acknowledgment that will fuel every future complaint from a researcher, a developer, or a company that finds its work echoed in a lab's output.
The commercial stakes here are larger than a single proof. Frontier labs are pitching agentic research as a product category — 10,000 concurrent agents grinding on a hard problem is the demo — and the willingness of academic researchers to route their draft work through Codex or Claude depends on whether they trust the pipeline. OpenAI's decision to skip the $1 million prize reads as an attempt to defuse the credit fight, but the harder question is whether serious mathematicians will keep uploading unpublished work into a system whose training window they cannot see. If the answer trends toward no, the next Navier-Stokes-scale claim will be produced against a much smaller pool of live human collaboration — and the labs will have made their own agents lonelier.
Working on something we should cover, or seeing a story we missed? Send leads, documents, or feedback to hello@aichatdaily.com. For sensitive tips, see our secure tips page for Signal and PGP options.
Spotted an error? Email hello@aichatdaily.com with the URL and the issue, or read our full corrections policy.
