Key facts
- NYU mathematician Tristan Buckmaster and Anthropic mathematician Levent Alpöge have announced proofs for the Navier-Stokes existence and smoothness problem.
NYU professor Tristan Buckmaster alleges OpenAI used unethical tactics, including potentially leveraging his team's progress and using extensive compute resources, to solve a major unsolved math problem. OpenAI denies the claims, calling them false and inflammatory.

This dispute raises critical questions about the ethical boundaries in AI-assisted mathematical research, the potential for AI models to inadvertently or intentionally replicate human work, and the competitive dynamics between leading AI labs.
NYU mathematics professor Tristan Buckmaster has announced significant progress on the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems, in collaboration with Anthropic mathematician Levent Alpöge. However, the announcement is overshadowed by a dispute with OpenAI, which Buckmaster accuses of employing unethical tactics.
Buckmaster stated that information about his team's progress was shared with OpenAI, after which OpenAI claimed to have independently solved the problem. He alleges that OpenAI used a large team and substantial computing power, potentially influenced by his team's approach, and became evasive when questioned about their methods. Buckmaster also raised concerns that OpenAI might have used his interactions with its Codex model to inform their solution, as OpenAI reserves the right to train on user data.
Sebastian Bubeck, who leads OpenAI's mathematical research, has refuted Buckmaster's claims, labeling them "false and inflammatory" and asserting adherence to academic standards. The controversy highlights the specific and uncommon approach Buckmaster and Alpöge took, making it suspicious to Buckmaster that OpenAI pursued the same path concurrently. Buckmaster further alleges that Bubeck attempted to pressure him by asking to remove Alpöge's credit and issuing veiled threats about his career if the dispute became public.
The Navier-Stokes problem, widely used in fluid mechanics, has a $1 million bounty from the Clay Mathematics Institute for its solution. Buckmaster's decision to publicize the dispute stems from a desire to counter what he perceives as potentially misleading announcements from OpenAI, emphasizing that he has not seen OpenAI's proof and is merely stating what he was told and proposed.