Tristan Buckmaster, a mathematics professor at New York University, revealed three new proofs addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems. Collaborating with Anthropic mathematician Levent Alpöge, Buckmaster utilized AI models including OpenAI's Codex and Anthropic's Claude to advance their research.
Shortly after their announcement, OpenAI published a full proof of the Navier-Stokes problem, claiming it was generated by an unreleased next-generation AI model. This effort reportedly consumed approximately 300 billion output tokens, equating to an estimated $22.5 million in compute costs.
The Navier-Stokes problem, fundamental to fluid mechanics, remains unsolved in theoretical mathematics, with a $1 million prize offered for a verified solution. Buckmaster's approach, focusing on a less common tactic involving smooth forces, was notably distinct and not widely pursued by other researchers.
Buckmaster alleges that OpenAI gained access to details about his and Alpöge's progress before it was made public. When questioned, OpenAI confirmed initiating their focused research on September 1, inspired by rumors of recent breakthroughs in Millennium Prize problems. However, OpenAI denied accessing any specific user data from Buckmaster's work, though they acknowledged that de-identified data from product usage might have indirectly influenced their models.
The situation has led to tensions between the parties. Buckmaster reports that OpenAI representatives requested removing Alpöge's credit from the work and cautioned against publicizing the dispute, suggesting potential career repercussions.
This episode highlights ongoing concerns about transparency, data usage, and competitive dynamics as AI increasingly contributes to complex mathematical research. Buckmaster advocates for openness to ensure fair recognition and to clarify AI's role in advancing such fundamental problems.