Tristan Buckmaster, a mathematics professor at New York University, revealed three proofs addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems, on Tuesday. Collaborating with Levent Alpöge from Anthropic and utilizing AI models including OpenAI's Codex and Anthropic's Claude, their work marks a notable advance in understanding a fundamental challenge in fluid mechanics and mathematical physics.
However, Buckmaster's announcement was accompanied by allegations that OpenAI leveraged knowledge of their progress to accelerate its own efforts. Shortly after Buckmaster's disclosure, 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 computational costs.
Buckmaster stated that information about his team's work had been shared with OpenAI before becoming public. When questioned, OpenAI acknowledged beginning its focused research on September 1, motivated by rumors of recent breakthroughs on Millennium Prize problems, and confirmed ongoing discussions with Buckmaster and Alpöge. Yet, details about the extent of human involvement and the timeline of OpenAI's research remain vague.
The Navier-Stokes problem involves proving the existence and smoothness of solutions to equations fundamental in fluid dynamics, a challenge that has eluded mathematicians for decades. Buckmaster and Alpöge pursued a less common approach, which they found suspiciously mirrored by OpenAI's model in a short timeframe.
Further complicating matters, Alpöge's affiliation with Anthropic, a competitor to OpenAI, appears to have been a point of contention. Buckmaster alleges that OpenAI representatives requested removing Alpöge's credit from their joint work and discouraged publicizing the dispute, warning of potential career repercussions.
Concerns also arose regarding OpenAI's use of Codex, as Buckmaster extensively employed this model in his research. Since OpenAI may train models on user interactions unless opted out, there is a possibility that their AI was indirectly informed by Buckmaster's work. OpenAI has denied accessing any specific user data prior to public release but acknowledged that de-identified data might have contributed to model improvements.
This episode highlights ongoing tensions about AI's role in advancing mathematical research and the ethical considerations surrounding collaboration, data usage, and credit attribution. Buckmaster advocates for transparency and openness to ensure fair recognition and to address the challenges posed by AI-driven research.
The controversy underscores the need for clear guidelines as AI increasingly intersects with academic discovery, particularly in high-stakes areas like the Millennium Prize problems.