On the Navier–Stokes Millennium Prize Problem
Simon Willison’s Weblog Simon Willison ● Covered by 7 sources
OpenAI used internal agent systems and large language models to reach and formally verify a result related to the Navier–Stokes Millennium Prize Problem after hearing rumors of Millennium Prize resolutions. The agents launched on September 1 and arrived at their resolution about 88 hours later, using 130 billion output tokens on Navier–Stokes. The dispute shifts to priority and possible data influence questions, while OpenAI says it did not access user data and still questions whether de-identified usage could have indirectly helped.
Why it matters
On the Navier–Stokes Millennium Prize Problem Impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems that have been subject to a $1,000,000 prize since May 24th, 2000. The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster, an NYU mathematics professor who was collaborating on related problems with Levent Alpöge, an accomplished mathematician who currently works for Anthropic. Tristan's complaint accompanied a hastily published version of their own results. Here's the PDF describing what happened. The very short version is that Tristan and Levent worked on the problem for almost a year, making extensive use of Claude and Codex (mainly GPT-5.6 Sol), then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear and Tristan and Levent heard that OpenAI had heard that Anthropic had resolved "a major open
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