NYU mathematician Jared Buckmaster and Anthropic mathematician Levent Alpöge released proofs using Codex and Claude AI models, but their announcement was accompanied by controversy. Buckmaster claims information about their research progress was leaked to OpenAI, prompting them to contact the company. OpenAI initially claimed to have already achieved a full proof of the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems worth $1 million. When pressed about when they began research and how much human input was involved, Buckmaster says OpenAI became evasive and eventually admitted their first prompt was sent only after learning about Buckmaster's work.
Buckmaster found it suspicious that OpenAI took the same mathematical approach—through a smooth force, options c and d in Fefferman's statement of the problem. He stated the route 'Luis and Diego opened and the one Levent and I had quietly chosen to attack' was nearly identical. Sebastian Bubeck, who leads OpenAI's mathematical research, called Buckmaster's claims 'false and inflammatory' and said he was 'disappointed' the dispute had escalated, adding that academic standards were 'of the highest importance' to him. He promised a more complete statement would follow.