On September 8, 2026, OpenAI revealed that it had resolved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems carrying a $1 million reward. The breakthrough was achieved using an internal, unreleased AI model that processed billions of tokens and millions of messages over several days.
The announcement has been met with controversy following allegations from Tristan Buckmaster, a mathematics professor at NYU, who collaborated with Levent Alpöge, a mathematician employed by Anthropic. Buckmaster and Alpöge had been working on related problems for nearly a year, utilizing AI tools including Claude and Codex, and reported a significant breakthrough in mid-August.
Buckmaster raised concerns that OpenAI may have accessed or been influenced by their unpublished work, noting that OpenAI did not clearly answer when their AI was first prompted or whether it had been trained on data from their sessions. OpenAI denied accessing any user-specific data but acknowledged that de-identified data might have contributed to model improvements. They also stated that their proofs differ significantly from those of Buckmaster and Alpöge.
OpenAI began their focused effort on September 1 after hearing rumors of breakthroughs on Millennium Prize problems. Their AI agents reached the Navier–Stokes resolution within days, followed by formal verification using GPT-6 Astra. The scale of computation was substantial, involving approximately 300 billion output tokens across all problems tackled.
The dispute highlights broader concerns about the use of proprietary data in AI training, especially when users employ AI tools to develop solutions to complex problems. It raises questions about intellectual property, data privacy, and the competitive dynamics between AI labs and researchers.
This incident also reflects a growing trend where knowledge of an unresolved problem can trigger extensive AI-driven exploration, potentially accelerating discoveries but complicating collaboration and credit attribution. The situation underscores the need for clearer policies on data usage and transparency in AI-assisted research.