OpenAI's Navier-Stokes proof sparks a dispute over stolen ideas

Tristan Buckmaster went public on Tuesday with preliminary proofs on the Navier-Stokes existence and smoothness problem, a feat that would settle one of mathematics' seven Millennium Prize problems and its $1 million bounty. Within days, OpenAI published its own complete proof of the same problem, and the NYU mathematician is now accusing the company of racing him unfairly to the finish line.

Buckmaster developed his results with Anthropic mathematician Levent Alpöge, using Codex and Claude models as research aids. He says he only reached out to OpenAI on September 3, after hearing that details of his and Alpöge's progress had already reached the company through informal channels.

OpenAI maintains that its latest push on the problem started on September 1, two days before that contact, using an internal model more capable than its newly released GPT-6 Astra. The company says it deployed 10,000 concurrent agents and burned through 300 billion output tokens over the following week, a run TechCrunch values at roughly $22.5 million at current Astra pricing.

The timeline is where the dispute gets messy. TechCrunch reports OpenAI has acknowledged that its first prompt on this attempt went out "in the past few days, after information about our work had reached OpenAI," a phrasing that sits awkwardly next to the company's stated September 1 start date. OpenAI has not clarified which account is accurate.

Buckmaster also points to methodology. He calls it suspicious that OpenAI's model converged on the same relatively uncommon proof strategy his team used, at nearly the same time. OpenAI's Sébastien Bubeck insists the two proofs "differ significantly" with distinct final results, but both efforts trace back to prior work by mathematicians Diego Córdoba and Luis Martínez-Zoroa on forced singularity formation, the same lineage Buckmaster cites as his own starting point.

Buckmaster wrote on Mastodon that OpenAI is "openly admitting they used training data from a period after we found our result."

Bubeck has said OpenAI "did not see any of their work until they released it publicly," yet OpenAI's own statement hedges: it says no specific user data was accessed to solve the problem, but concedes it "cannot rule out that de-identified data derived from their usage of our products helped improve our models." Buckmaster asked directly whether the internal model had trained on or accessed his and Alpöge's Codex sessions and says he got no clear answer.

OpenAI's internal model, which began training August 28, reportedly showed unusual strength on math benchmarks even before this episode. The company has said it will not pursue the Clay Mathematics Institute's $1 million prize itself, leaving the credit dispute as the more immediate fallout for a field where AI-assisted proofs are becoming harder to disentangle from human ones.