OpenAI, mathematician clash over AI's Navier-Stokes proof claim

A mathematician says artificial intelligence has been used to crack the Navier-Stokes equations, one of the Clay Mathematics Institute's six 'million-dollar' problems in fluid dynamics, according to Scientific American. The reporting frames it as possibly 'the biggest day in math in at least two decades,' and it arrives bundled with a priority dispute that has consumed the field in a matter of days.

Tristan Buckmaster says he and Levent Alpöge, an Anthropic employee, used Anthropic's LLMs to prove on August 15 that the simpler Euler equations 'blow up' (admit singular solutions), a step toward the full Navier-Stokes problem. Over the past weekend, an OpenAI team reportedly used the company's own internal model to extend the argument to Navier-Stokes itself. Buckmaster posted his account at 11:58 P.M. EDT on Monday.

'This is a Deep Blue–Kasparov moment,' Buckmaster wrote, invoking the chess match that heralded machine dominance over humans. He alleges that OpenAI, on learning of his and Alpöge's work in progress, moved rapidly to finish the proof and, in a phone call with the company's math-team lead Sébastien Bubeck, was offered sole authorship on a version that excluded Alpöge.

Two caveats sit next to the celebration. The proof leans on the 'forcing' technique developed by Diego Córdoba and Luis Martínez-Zoroa, and it exploits a term in the Clay problem statement that most experts typically leave out. Per the article, 'The Clay problem, as written, is solved. But the Clay problem, as many experts imagine it, lacks the piece that the forcing method relies on.' Verification of the underlying reasoning was done in the proof-assistant language Lean, but the article notes that 'the English-language explanation the LLMs produced was barely readable' and had to be reconstructed by hand.

Buckmaster's own reading of the episode is not centered on the credit fight: 'There is a far bigger story here than the one in my statement: the sheer magnitude of what frontier models can now do, and what that means for us all.'