Tristan Buckmaster, a mathematics professor at New York University, announced three proofs addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems in mathematics. The work was conducted alongside Anthropic mathematician Levent Alpöge, using AI models including OpenAI's Codex and Anthropic's Claude. While the proofs themselves mark a significant step in theoretical mathematics, the announcement also revealed a contentious dispute involving OpenAI.
Buckmaster stated that during the final stages of their research, information about their progress was shared with OpenAI. Upon inquiry, OpenAI claimed to have already completed a full proof of the problem. However, when pressed for details about the timeline and human involvement in OpenAI's research, responses were vague. Buckmaster alleges that OpenAI had access to their approach and used substantial computational power to finalize a proof shortly after learning of their work.
Sebastian Bubeck, leading OpenAI's mathematical research, refuted these claims as "false and inflammatory," emphasizing his commitment to academic standards and promising a fuller response.
The Navier-Stokes problem, central to fluid mechanics and mathematical physics, remains unsolved despite extensive efforts. Buckmaster and Alpöge pursued a less common approach involving a smooth force, which they say was not widely explored by others. This makes OpenAI's parallel adoption of the same method within a short timeframe particularly suspicious to them.
Alpöge's affiliation with Anthropic, a competitor to OpenAI, added complexity to the situation. Buckmaster alleges that Bubeck requested Alpöge's credit be removed from the research, and that attempts were made to discourage public discussion of the dispute, with warnings about potential career damage.
Another concern raised involves OpenAI's use of Codex, which can be trained on user interactions unless opted out. Buckmaster worries that OpenAI's models may have incorporated data from his own Codex usage, potentially influencing their proof. OpenAI has not commented on this possibility.
This controversy highlights ongoing questions about the role of AI in advancing mathematical research and the ethical considerations around collaboration, data usage, and credit. Buckmaster advocates for transparency, stating he has not seen OpenAI's proof and does not accuse anyone but wishes to correct misinformation circulating publicly.