OpenAI solution for the Navier-Stokes problem overshadowed by plagiarism controversy — researcher working on related proof claims his work with Codex influenced OpenAI's direction

Most anyone involved in computing has heard about the P-NP problem, but fluid engineers and mathematicians would love to know if the Navier-Stokes equations have smooth, globally defined solutions. Both questions are part of the Millennium Prize Problems, solutions to which are worth a cool $1 million and eternal renown. OpenAI is claiming that its staff and internal models have solved the conditions of Navier-Stokes solutions set forth in the Millennium Prize. But the company's shouting from the rooftops is being met with a chorus of boos over claims it might have plagiarized the work of a research team that had been toiling on a related, stepping-stone problem for a year.

Tristan Buckmaster (a scientist at NYU) and Levent Alpöge (a member of Anthropic's staff) had been quietly working on proving Euler's equations — another long-standing mathematical problem, and one that is generally acknowledged to be a stepping stone to solving Navier-Stokes.

According to Buckmaster, his work with Alpöge was "a purely personal collaboration, free of any institutional agreements or official involvement by either of our employers." The researchers used Anthropic Claude and OpenAI Codex as assistants, as is apparently now common in the field, to perform busywork (documentation, searching, etc.) as well as running through logic steps. The substantial amount of compute time the project required was paid from Buckmaster's own pockets, too.