AI math breakthrough sparks controversy
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The gist
OpenAI claims its AI made progress on the Navier-Stokes equations in 88 hours.
The claim is disputed over credit and data use, and awaits peer review.
Background
The Navier-Stokes existence and smoothness problem is one of the Clay Mathematics Institute's Millennium Prize problems, carrying a $1 million reward. On September 8, 2026, NYU professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge announced three new proofs advancing understanding of the problem, achieved using OpenAI's Codex and Anthropic's Claude. OpenAI separately claimed its internal AI system made progress on the same problem in 88 hours, producing 2.7 million messages and about 130 billion tokens. The dispute centers on whether OpenAI used unpublished research by Buckmaster and Alpöge, who had been working on a related problem for about a year.
How it unfolded
- Sep 3, 2026Buckmaster discovered that details of his and Alpöge's research progress had been transmitted to OpenAI.
- Sep 6, 2026Buckmaster spoke by phone with Sébastien Bubeck, who leads OpenAI's math team, and another OpenAI employee; Buckmaster alleges the call became contentious, with OpenAI offering him sole authorship for the Navier-Stokes result in a paper acknowledging the company's internal model had solved it, and Bubeck allegedly wanting to exclude Alpöge.
- Sep 8, 2026Buckmaster and Alpöge announced three new proofs advancing the Navier-Stokes problem, achieved using OpenAI's Codex and Anthropic's Claude. OpenAI separately claimed its internal AI system made progress on the problem in 88 hours.
- Sep 9, 2026Media reports described the controversy over credit and whether OpenAI accessed unpublished work; OpenAI maintained it did not access specific user data before the public release of Buckmaster and Alpöge's work.
Who’s saying what
- OpenAI
- OpenAI maintains that it did not access specific user data before the public release of Buckmaster and Alpöge's work, and claims its internal model made progress on the problem in 88 hours.
- Buckmaster
- Buckmaster alleges that OpenAI redirected its research toward the problem after learning of his and Alpöge's work, and questions whether private material from Codex played a role.
- Mathematicians
- Some mathematicians say the claim is being overstated before peer review, and that OpenAI's refusal to release the proof publicly raises questions.
- Analysts
- The dispute raises questions about the ethics of using proprietary AI tools for scientific research and whether private uploaded drafts remain secure.
Still unverified
Buckmaster's allegations that OpenAI accessed his unpublished work and that Bubeck wanted to exclude Alpöge are based on his account and have not been independently confirmed. OpenAI's claim that its AI solved or made progress on the Navier-Stokes problem has not been peer-reviewed or publicly released in full. Reports describe the proof as unverified and the controversy as ongoing.