OpenAI announced significant progress on the Millennium Prize Problems

OpenAI stated to The New York Times that since announcing progress on the Navier-Stokes equations on September 8, it has made "substantial progress" on one of the Millennium Prize Problems, but did not disclose which specific problem it is or provide a timeline for disclosure. The Millennium Prize Problems are seven mathematical problems established by the Clay Mathematics Institute since 2000, each with a reward of one million dollars.

Speculation suggests that the problem may be the Hodge Conjecture, a 76-year-old problem regarding how to calculate the number of "holes" in complex geometric shapes. OpenAI has not confirmed this speculation and has not responded to rumors that its underlying model is a version of Aeon specifically designed for long-duration tasks. Previously, on September 8, OpenAI announced that its unreleased internal model generated a proof verified by Lean, indicating that the Navier-Stokes equations could "blow up" to physically impossible infinite speeds, involving about 10,000 coordinated AI agents and taking approximately 88 hours.

However, this statement has sparked controversy. New York University mathematician Tristan Buckmaster stated that he and Anthropic researcher Levent Alpöge had been working on the related proof for nearly a year prior and completed it on August 22, while OpenAI's Sébastien Bubeck published his findings first upon learning of it. OpenAI stated that it is not pursuing the one million dollar prize, but rather using these problems as a public benchmark to measure the speed of model progress. The review of the Navier-Stokes proof by the Clay Mathematics Institute is still ongoing, and verification of past Millennium Prize Problems typically takes several years.