OpenAI Says It Has Made Major Progress on Second Millennium Prize Problem

OpenAI told The New York Times that it has made "substantial progress" on a second Millennium Prize Problem since announcing a solution to the Navier-Stokes equations on September 8, without disclosing which problem it is or providing a timeline for release. The Millennium Prize Problems are seven $1 million math challenges established by the Clay Mathematics Institute since 2000. Outside speculation suggests the problem could be the Hodge Conjecture, a 76-year-old challenge about how to calculate the number of "holes" in complex geometric shapes. OpenAI did not confirm this speculation, nor did it respond to rumors that the underlying model is a version of Aeon, designed for long-duration tasks. Previously, on September 8, OpenAI announced that its unreleased internal model generated a Lean-verified proof showing the Navier-Stokes equations could "blow up" into physically impossible infinite velocities, a process involving approximately 10,000 coordinated AI agents over about 88 hours. However, that announcement sparked controversy. New York University mathematician Tristan Buckmaster said he and Anthropic researcher Levent Alpöge had been working on a related proof for nearly a year, completing it on August 22, and that OpenAI's Sébastien Bubeck learned of it and rushed to publish first. OpenAI stated it is not pursuing the $1 million prize, but rather using these problems as a public benchmark to measure the pace of model progress. The Clay Mathematics Institute's review of the Navier-Stokes proof is still ongoing, and verification of past Millennium Problems has typically taken several years.