OpenAI reports significant progress on the second Millennium Prize Problem

ChainCatcher report: OpenAI told The New York Times that since announcing on September 8 that it had solved the Navier-Stokes equations, it has made "substantial progress" on a second Millennium Prize Problem—but did not disclose which problem or provide a timeline for disclosure. The Millennium Prize Problems are seven mathematical challenges, each with a $1 million reward, established by the Clay Mathematics Institute since 2000. Outside observers speculate the problem may be the Hodge Conjecture, a 76-year-old problem concerning how to count "holes" in complex geometric shapes. OpenAI has not confirmed this speculation nor responded to rumors that its underlying model is an Aeon version designed for long-duration tasks. Previously, on September 8, OpenAI announced that its unreleased internal model generated a Lean-verified proof suggesting the Navier-Stokes equations might "blow up" into physically impossible infinite velocities, involving approximately 10,000 coordinated AI agents over roughly 88 hours. However, this announcement sparked controversy: New York University mathematician Tristan Buckmaster stated that he and Anthropic researcher Levent Alpöge had been working on the same proof for nearly a year prior and completed it on August 22, after which OpenAI’s Sébastien Bubeck learned of it and published first. OpenAI stated it was not motivated by the $1 million prize but rather intended these problems as public benchmarks to measure the speed of model progress. The Clay Mathematics Institute’s review of the Navier-Stokes proof is still ongoing; verification of past Millennium Prize Problems has typically taken several years.