OpenAI says it cracked the Navier-Stokes existence and smoothness problem, a mathematical puzzle that has baffled experts for roughly 90 years. The company announced the feat in a blog post Tuesday, crediting an internal AI model that outperforms GPT-6 Astra and utilized 10,000 concurrent agents to navigate the complex fluid dynamics equations. This isn’t just a theoretical win; the Navier-Stokes equations govern how liquids and gases flow, making them critical for everything from weather forecasting to aircraft design. Solving it is one of the seven Millennium Prize Problems, each carrying a $1 million reward from the Clay Mathematics Institute.
But the celebration hit a snag almost immediately. Just one day prior, NYU professor Tristan Buckmaster and Anthropic researcher Levent Alpöge published findings on a related aspect of the problem. Buckmaster alleges that OpenAI’s solution mirrors the specific route he and Alpöge were developing using OpenAI’s Codex and Anthropic’s Claude. He claims he reached out to OpenAI after hearing rumors of their progress, asking directly if their private drafts in Codex had been used to train the model. “I was told the model did not look up user data,” Buckmaster wrote. “I asked again, about training, and I did not get an answer.”
OpenAI moved quickly to deny any direct misuse of private data. Sebastien Bubeck, a technical staff member at OpenAI, stated they didn’t see Buckmaster and Alpöge’s work until it went public, noting that the proofs differ significantly. The company clarified that while no specific user data was accessed to solve the problem, they “cannot rule out that de-identified data derived from their usage of our products helped improve our models.” Buckmaster pushed back on Mastodon, arguing this admission confirms OpenAI used training data from the period after their result was found.
This incident highlights a growing tension in AI-assisted research: where does collaborative tool use end and intellectual property infringement begin? If OpenAI’s models ingested private coding sessions to learn mathematical reasoning patterns, even without direct access to the final proof, the line between inspiration and appropriation blurs. OpenAI says it won’t claim the $1 million prize, perhaps to avoid further scrutiny, but the mathematical community is left debating whether this is a genuine AI breakthrough or a sophisticated case of accidental plagiarism.
