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Tristan Buckmaster, a mathematics professor at NYU, unveiled three proofs on Tuesday that offer preliminary insights into one of the most pressing unresolved questions in theoretical mathematics. Teaming up with Levent Alpöge, a mathematician at Anthropic, and using the capabilities of AI models like Codex and Claude, the findings hold significant mathematical weight yet are clouded by a distinctive controversy involving OpenAI’s competing attempts to tackle the same problem.
In his public statement announcing the proofs, Buckmaster expressed his concern over a parallel effort by OpenAI, suggesting that they accessed insights from his research prior to its release. This led to a complex web of academic rivalries and conflicting assertions.
Shortly after Buckmaster’s disclosure, OpenAI shared a comprehensive proof regarding the Navier-Stokes existence and smoothness issue, which has vast implications in fluid mechanics and is one of the seven Millennium Prize problems – each with a $1 million reward for a solution. OpenAI contended that their achievement stemmed from an advanced, unreleased model that has made strides on a high number of unsolved tasks over the past week, consuming roughly 300 billion tokens, or about $22.5 million in computational costs, if billed at current Astra rates.
As Buckmaster and Alpöge finalized their results, they discovered that OpenAI had received information about their progress. When they inquired about the timeline of OpenAI’s work and the involvement of human input, the responses were less than clear. Buckmaster noted that OpenAI had been working intensely on the problem and used an extensive amount of resources in their pursuit of a formal proof.
This revelation suggests that OpenAI may have felt validated by Buckmaster and Alpöge’s approach and decided to leverage its computational advantage to complete the proof first. OpenAI’s recent post corroborates this timeline, stating their efforts kicked off on September 1 and were partly inspired by speculation regarding solutions to two Millennium Prize problems, while acknowledging ongoing discussions with Buckmaster and Alpöge.
Despite the widespread interest among mathematicians, the specific strategy employed by Buckmaster and Alpöge is relatively unique. Buckmaster found it particularly suspicious that OpenAI pursued a similar method at once. He asserted that the pathway they chose, which involves a smooth force component in the Navier-Stokes equations, is one less commonly explored by others in the field.
Though Alpöge is affiliated with Anthropic, he conducted this research independently, primarily using OpenAI’s Codex. This circumstance became a point of contention, particularly when Buckmaster alleged that an OpenAI representative requested the removal of Alpöge’s acknowledgment as part of a proposed compromise.
When Buckmaster insisted on making the dispute public, he faced veiled threats regarding his career. He later expressed concern that his extensive use of Codex may have inadvertently informed OpenAI’s efforts to derive a solution to the problem. Although OpenAI asserts that no specific user data from Buckmaster’s work was accessed, they acknowledge that de-identified data derived from product usage could potentially enhance their models.
OpenAI’s stance contrasts with Buckmaster’s misgivings and is likely to reignite discussions about the role of artificial intelligence in mathematical exploration, along with the company’s motivations in this area. As the situation unfolds, Buckmaster aims to promote transparency about the research to foster a more informed dialogue.
