NYU mathematics professor Tristan Buckmaster, along with Anthropic mathematician Levent Alpöge, recently announced significant preliminary proofs addressing the Navier-Stokes existence and smoothness problem, one of the Millennium Prize unsolved math problems. Their collaborative work utilized AI models including OpenAI’s Codex and Anthropic’s Claude, marking a major step forward in the theoretical understanding of fluid mechanics. However, Buckmaster’s statement revealed a contentious situation involving OpenAI’s parallel efforts to solve the same problem, which he described as “fighting dirty.”

OpenAI published a full proof shortly after Buckmaster’s announcement, claiming the breakthrough came from an unreleased next-generation AI model that had expended $22.5 million in computing costs over a week, processing 300 billion output tokens. Buckmaster alleges that OpenAI’s team started its latest work only after getting wind of his and Alpöge’s approach and that they adopted a similar uncommon method to solve the problem. He also criticized OpenAI for a lack of transparency regarding the timing and amount of human input involved and raised concerns about potential conflicts stemming from Alpöge’s Anthropic affiliation.

The dispute extended to internal dynamics, where Buckmaster alleges OpenAI mathematician Sébastien Bubeck tried to exclude Alpöge’s credit and discouraged Buckmaster from publicizing the disagreement, implying career risks. Buckmaster posits that OpenAI might have leveraged data from his Codex interactions—information that OpenAI’s policy allows for model training unless users opt out—potentially influencing their final proof. OpenAI denied accessing specific user data but acknowledged that de-identified data might have indirectly improved their models, while emphasizing differences between their and Buckmaster’s proofs.

This controversy highlights ongoing tensions around AI’s evolving role in high-stakes mathematical research and the ethical challenges posed by competitive pressures in AI development. With the Navier-Stokes problem carrying a $1 million Clay Mathematics Institute prize for a verified solution, the race between individual mathematicians and powerful AI labs raises questions about credit, transparency, and collaboration in advancing scientific knowledge. Buckmaster advocates for increased public disclosure of research details to foster openness amid these disputes.