New York University mathematician Tristan Buckmaster has announced three proofs, including a preliminary result tied to one of theoretical mathematics' most closely watched open questions. The work was developed with Anthropic mathematician Levent Alpöge and supported by AI tools from both Codex and Claude.
The announcement also drew attention because Buckmaster says information about his team's progress reached OpenAI while the research was still being finalized. According to his account, OpenAI later claimed to have produced a full proof of the central problem, prompting questions about timing, research methods, and the role of human guidance in AI-assisted mathematics.
The discussion centers on the Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute's Millennium Prize Problems. The challenge is deeply important in fluid mechanics and mathematical physics, and a verified solution would mark a major step forward in the field.
Buckmaster argues that the route he and Alpöge chose was uncommon, which made the overlap with OpenAI's approach especially notable. OpenAI's mathematical research lead Sebastian Bubeck has rejected the criticism, calling the claims false and inflammatory, while saying a fuller response would follow.
The episode adds momentum to a broader conversation about how AI can support advanced research while preserving academic norms, attribution, and transparency. As these tools become more capable, they may reshape the pace and style of discovery in mathematics and beyond.
