OpenAI has told The New York Times that it has made “substantial progress” on a second Millennium Prize Problem, days after saying it had solved the Navier–Stokes problem. The company has not identified the problem or provided a timeline for disclosing its work.

Online speculation, which OpenAI has not confirmed, has focused on the Hodge Conjecture, a 76-year-old mathematical question concerning how to count the “holes” in complex geometric shapes. The conjecture, proposed by mathematician William Hodge in 1950, suggests that algebra can provide a shortcut for analyzing geometric structures. No one has proved that the shortcut works in every case.

The seven Millennium Prize Problems were established by the Clay Mathematics Institute in 2000, with a $1 million prize associated with each problem. Only one of the seven, the Poincaré Conjecture, has ever been solved, and the institute’s guidelines require a proposed solution to gain acceptance within the mathematics community before a prize can be awarded. OpenAI says it is not pursuing the money. Instead, the company has described the problems as a public benchmark for measuring how quickly its models are improving.

OpenAI has also not confirmed speculation that an unreleased model involved in the work is a version called “Aeon,” reportedly designed for long-horizon tasks and agentic workflows. Both the Hodge Conjecture theory and the Aeon reports remain unverified and are not company statements.

One social media post cited in the speculation said:

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"
— leo 🐾 (@synthwavedd) September 3, 2026

https://x.com/synthwavedd/status/2095536656023470365?ref_src=twsrc%5Etfw

OpenAI’s earlier Navier–Stokes announcement said an unreleased internal model had produced a proof verified in Lean, software that checks mathematical proofs one logical step at a time. Because such software checks each step mechanically, a completed Lean proof can be re-checked by others rather than taken on trust. The proof concerned whether the Navier–Stokes equations—which describe the movement of fluids such as air and water—can “blow up” into a physically impossible infinite speed. OpenAI said the effort involved roughly 10,000 coordinating AI agents working for about 88 hours. The equations are important to aircraft design, weather and the modeling of blood flow, and they had resisted a complete mathematical explanation for nearly 90 years. OpenAI’s announcement is available at OpenAI.

The Clay Mathematics Institute has not completed its review of OpenAI’s Navier–Stokes proof. A separate dispute over credit also remains unresolved. NYU mathematician Tristan Buckmaster said in a four-page statement that he and Anthropic researcher Levent Alpöge had worked on a related proof for almost a year and completed it by August 22, before OpenAI’s Sébastien Bubeck learned of their work and attempted to publish first.

Buckmaster said Bubeck told him either to allow OpenAI to publish the day after his team or to write the paper alone, without Alpöge, because Alpöge worked for a competing laboratory. Buckmaster said Bubeck allegedly asked him, “Why would you ruin your career?”

The developments come as AI companies pursue increasingly difficult mathematical tasks. Anthropic said during the same week that its Claude model formalized a 358-year-old proof of Fermat’s Last Theorem in 11 days. Mathematician Terence Tao has warned that competition among AI laboratories could consume the supply of difficult, useful mathematical problems faster than new ones can be found.

The next test for OpenAI’s claims will be independent verification by the Clay Mathematics Institute or outside mathematicians. Reviews of previous Millennium Prize submissions have taken years rather than weeks, and the second problem will face the same hurdle once OpenAI identifies it and discloses its work.