OpenAI Claims Navier-Stokes Breakthrough, but Dispute Over Data Access Clouds Milestone

OpenAI announced this week that its internal AI system has cracked the Navier-Stokes problem, a mathematical puzzle that has stumped researchers for roughly nine decades. The problem deals with understanding how liquids and gases flow, and sits among seven Millennium Prize Problems — each valued at $1 million for its solution. The company trained its proprietary model starting August 28th and deployed 10,000 concurrent AI agents to work through the challenge.

The Breakthrough and Its Stakes#

The solution represents a significant milestone for the mathematics and AI communities. OpenAI published details of its approach in a blog post, underscoring that the internal model "exhibited unprecedented performance in our benchmarks, including mathematics." The company has stated it will not claim the $1 million prize despite solving the problem.

Allegations of Data Misuse#

However, the announcement has been shadowed by a dispute over how OpenAI obtained the solution. Just a day before OpenAI's Tuesday statement, NYU mathematics professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published their own findings on a closely related mathematical challenge. Buckmaster subsequently raised concerns that OpenAI may have accessed research materials he and Alpöge had uploaded to OpenAI's Codex tool during their work on the problem.

In a public statement, Buckmaster described asking OpenAI whether the model had been trained on or had access to their Codex sessions. He reported receiving evasive responses: "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer."

OpenAI's Defense#

OpenAI countered by stating that "no specific user data was accessed in order to solve this problem," though it acknowledged an important caveat: "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Sebastien Bubeck, a member of OpenAI's technical staff, added that the company did not see Buckmaster and Alpöge's work until they made it public and noted that "our proofs differ significantly and even the precise results proved are different."