OpenAI and the Navier-Stokes controversy

OpenAI threatens to ruin mathematician's career if he and his collaborator publish proof of a Millennium Prize problem. Tristan Buckmaster, a professor at NYU, and his collaborator, Anthropic mathematician Levent Alpöge, who believe they have solved the Navier-Stokes Millennium Prize problem, were threatened by OpenAI to either let OpenAI publish the proof, or acknowledge that an internal OpenAI model had helped them solve it. The Navier-Stokes equations are a system of partial differential equations that explain the flow of a fluid in space. Mathematicians are concerned with whether these equations always yield well-behaved, smooth solutions, or whether they "blowup", resulting in singularities where the fluid velocity becomes infinite in finite time. Buckmaster and Alpöge believe they have found a blowup. Their proof, still being verified in Lean, has not yet been published. In formulating the proof, they built on the work done by Diego Cordoba and Luis Martinez-Zoroa, using LLMs (including Claude, Sol, and Astra). At the same time, OpenAI has announced that an unreleased internal model has found a blowup for Navier-Stokes. They have published a paper as well as a Lean formalization. This has raised a priority dispute, and OpenAI is accused of having used the mathematicians' work as training data. OpenAI's response is that the methods differ; while the mathematicians had a forced blowup, OpenAI's proof is unforced. However, when Levent inquired OpenAI for the precise statement, the answer was: "Existence of forced blowup in R 3 and T 3 ” with “the forcing function is smooth option c and d in Fefferman." When pushed by the mathematicians, OpenAI gave them two options: either let OpenAI publish the paper first, or publish the paper citing their internal model had resolved it. Buckmaster has refused both options. In return, OpenAI has threatened Buckmaster with ruining his career.