Overview
- OpenAI informed the New York Times of its "substantial progress" on a second Millennium Prize Problem, having recently solved the Navier-Stokes equations on September 8, though it did not specify the problem or a timeline for disclosure.
- Speculation on social media, which has not been confirmed by OpenAI, suggests that the problem might be the Hodge Conjecture, a 76-year-old enigma regarding the counting of "holes" in complex geometric structures.
- The Clay Mathematics Institute is still reviewing OpenAI's proof regarding the Navier-Stokes equations, and a dispute over credit with mathematician Tristan Buckmaster is yet to be resolved.
OpenAI continues to engage with some of the most challenging questions in mathematics, primarily seeking recognition rather than financial gain from these endeavors.
Shortly after announcing its solution to the Navier-Stokes equations, OpenAI revealed to the New York Times that it has made significant strides on another Millennium Prize Problem, which is one of seven major mathematical challenges that the Clay Mathematics Institute has offered a $1 million reward for since 2000.
Myriad: Which companies will IPO first? Click to make your prediction.While OpenAI has not disclosed which problem it is addressing, experts, enthusiasts, and journalists are speculating about potential candidates.
Much of the online discussion has centered on the Hodge Conjecture, a mathematical challenge from 1950 concerning how to determine the number of "holes" in complex shapes that are difficult to visualize. Mathematician William Hodge proposed using algebraic methods instead of geometric ones to tackle this problem, but proving that the shortcut is universally applicable remains unresolved.
OpenAI has neither confirmed this theory nor the rumors surrounding the unreleased model believed to be connected to this work, referred to as the Aeon version, designed for long-term tasks and complex workflows. These remain speculative and not official statements from the company.
gpt-6-astra
gpt-6-astra-aeon^ new slugs added to a statsig feature flag that appeared ~30 mins ago in Codex Desktop
"aeon" means "an immeasurably or indefinitely long period of time, an age, or eternity"
â leo đŸ (@synthwavedd) September 3, 2026
On September 8, OpenAI announced that an internal model had generated a Lean-verified proofâLean being software that checks mathematical proofs step by stepâindicating that the Navier-Stokes equations could lead to an implausible infinite speed. Achieving this required approximately 10,000 AI agents collaborating over 88 hours.
This accomplishment holds significance beyond mathematics; the Navier-Stokes equations are fundamental in fields like aircraft design, weather predictions, and medical modeling of blood flow, and had eluded a complete mathematical explanation for nearly nine decades.
However, the announcement was marred by controversy. NYU mathematician Tristan Buckmaster detailed his perspective in a four-page statement, asserting that he and Anthropic researcher Levent Alpöge had been pursuing a related proof for nearly a year, completing it on August 22âprior to OpenAI's SĂ©bastien Bubeck's knowledge and subsequent rush to publish first.
Buckmaster alleges that Bubeck urged him to either allow OpenAI to publish the day after his team or to proceed alone, excluding Alpöge due to his affiliation with a competing lab. Buckmaster recounted that Bubeck questioned, "Why would you ruin your career?" when Buckmaster declined this option.
The emergence of powerful AI models is revitalizing interest in mathematics. In the same week, Anthropic reported that its Claude model had formalized a 358-year-old proof of Fermat's Last Theorem in just 11 days, while mathematician Terence Tao cautioned that the competitive race among AI labs is depleting the pool of challenging and valuable mathematical problems faster than new ones can be discovered.
OpenAI maintains that it is not pursuing the $1 million prize for publishing any result; instead, it uses these problems as benchmarks to gauge the progress of its models. The next test will be whether the Clay Institute or any independent mathematician can verify any of OpenAI's claimsâa process that has historically taken years rather than weeks for previous Millennium Prize submissions.