NYU Mathematician Alleges OpenAI 'Fought Dirty' in High-Stakes Math Challenge

NYU mathematics professor Tristan Buckmaster, in collaboration with Anthropic mathematician Levent Alpöge, recently announced three proofs with preliminary findings on the Navier-Stokes existence and smoothness problem, one of the major unsolved problems in theoretical mathematics. Their work notably utilized both Codex and Claude AI models, marking a significant advancement. However, this scientific breakthrough has been overshadowed by an unusual controversy involving OpenAI, who are accused of having pursued a parallel effort based on Buckmaster and Alpöge's yet-to-be-publicized work.

Buckmaster's public statement expressed his reluctance to address this 'other part of this story.' He revealed that information regarding their progress was allegedly passed to OpenAI, leading to a complex situation of academic rivalry and conflicting claims. Shortly after Buckmaster's announcement, OpenAI published a full proof of the Navier–Stokes problem, claiming it was discovered by an unreleased next-generation model. This effort reportedly consumed 300 billion output tokens, an expenditure estimated at $22.5 million if charged at current Astra rates, showcasing OpenAI's immense computational power.

The Navier-Stokes existence and smoothness problem is one of the seven Millennium Prize problems, each offering a $1 million reward from the Clay Mathematics Institute for a solution. These equations are fundamental to fluid mechanics, yet their theoretical understanding remains poor. A definitive solution would profoundly advance mathematical physics. Buckmaster and Alpöge learned of OpenAI's parallel work while finalizing their own results and, upon contacting OpenAI, were informed that a full proof had already been achieved. However, OpenAI's responses became evasive when asked about the commencement of their research and the extent of human involvement.

Buckmaster stated that it emerged an entire team at OpenAI had been working on the problem, using an 'insane amount of compute.' It was eventually agreed that the initial prompt sent to OpenAI's models occurred 'in the past few days,' after information about Buckmaster and Alpöge's work had reportedly reached them. This timeline suggests that OpenAI might have been influenced by their approach and leveraged its superior computing resources to arrive at a formal proof first. OpenAI's own post largely confirms this timeline, noting their latest effort began on September 1, inspired by rumors of two Millennium Prize problems being solved, and also acknowledges ongoing conversations with Buckmaster and Alpöge.

A critical point of contention lies in the specific strategy adopted. While the Navier-Stokes problem is widely pursued, the particular 'smooth force' approach (options c and d in Fefferman's statement of the problem) taken by Buckmaster and Alpöge is far less common. Buckmaster found it highly suspicious that OpenAI adopted the same niche method concurrently, stating, 'Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement.'

Adding to the complexity, although Alpöge is affiliated with Anthropic, a rival lab, his research was independent of his employer. The duo primarily used OpenAI's Codex in their work. Buckmaster further alleged that OpenAI's Bubeck attempted to pressure him into removing Alpöge's credit as part of a proposed compromise, and when Buckmaster threatened to make the dispute public, Bubeck reportedly responded with intimidating remarks like, 'Why would you ruin your career?' and 'If you don’t want me to be nice, then I don’t have to be nice.'

Buckmaster also raised concerns about potential information leakage, given his extensive use of Codex. OpenAI reserves the right to train models on Codex interactions, although users can opt-out. He speculated that if OpenAI's team used a model trained on his own Codex interactions, it could have potentially 'regurgitated' his work when faced with a similar problem. OpenAI, in its post, downplayed this possibility, stating that their researchers and agents 'did not see any of their work through any means until they released it publicly,' and that 'no specific user data was accessed.' They acknowledged, 'While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.' However, OpenAI emphasized that their proofs 'differ significantly' and even the precise results proved are different in the Euler case (forced vs unforced).

This entire incident is expected to reignite the broader debate concerning AI's evolving role in fundamental mathematical research and the specific incentives guiding organizations like OpenAI. Buckmaster, for his part, appears committed to ensuring that as much information about this research and the surrounding controversy is made public as possible.