OpenAI claims Navier–Stokes proof; NYU pair disputes credit

OpenAI says it has solved the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems, using an unreleased model. The announcement arrives tangled in a priority dispute with two mathematicians who say they were racing to the same result.

In his post walking through the timeline, Simon Willison relays accusations from Tristan Buckmaster, an NYU mathematics professor collaborating with Levent Alpöge, "an accomplished mathematician who currently works for Anthropic." The pair had worked the problem for nearly a year using Claude and Codex, then hit a breakthrough on August 15th. Buckmaster's "complaint accompanied a hastily published version of their own results," Willison writes.

OpenAI's own account, as Willison relays it, launched agents on September 1st after hearing rumors that two Millennium Prize problems had been resolved. Navier–Stokes fell 88 hours later, on September 5th, with Lean formalization completing on September 6th in 17 hours. The run consumed 2.7 million messages and roughly 130 billion output tokens; the wider effort came to about 4.9 million messages and 300 billion output tokens, an estimated $15,000,000 at public API prices. OpenAI acknowledged that "while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

Willison then poses the question the episode forces on any researcher using a frontier chatbot: "If I use ChatGPT to help me partially solve a Millennium Prize question, what are the chances that my work will influence training such that a later model helps someone else solve it first?" He nods to Anil Madhavapeddy's parallel framing that "just a rumour of a bug is enough to find a security exploit." Two experts in our Who's Who directory shared the source link.