OpenAI Says It's Made Progress on a Second $1 Million Math Problem

Days after saying an internal model produced a Lean-verified result for the Navier-Stokes equations, OpenAI informed the New York Times that it has also made substantial progress on a second of the Clay Mathematics Institute's seven Millennium Prize Problems. The company did not disclose which problem it means or when it might release details, leaving observers and reporters to parse clues and social-media discussion for hints. Much of the online speculation has pointed to the Hodge Conjecture, a long-standing 1950s-era question about classifying certain multidimensional "holes" in complex geometric objects using algebraic methods. OpenAI has not confirmed that conjecture is the target, nor has it verified which internal model produced the new work; some commentators have linked the reports to a rumored model variant called "Aeon," but those associations remain unverified by the company. OpenAI's earlier Navier-Stokes announcement has already stirred controversy and scrutiny. The company said an unreleased model produced a computer-checked proof in the Lean proof assistant showing that solutions to Navier-Stokes can "blow up;" OpenAI described the computation as involving roughly 10,000 coordinating AI agents running about 88 hours. The Clay Mathematics Institute has not yet completed its review of that submission, and the broader mathematical community has not independently confirmed the result. The Navier-Stokes episode also triggered a dispute over credit. NYU mathematician Tristan Buckmaster released a statement asserting that he and an Anthropic researcher had been developing a related proof before OpenAI's announcement and that there were disagreements about publication and attribution. OpenAI has said it is not pursuing the $1 million prize associated with the Millennium Problems and uses the challenges primarily as benchmarks for model capability. Any claim of a formal solution will depend on independent verification by outside mathematicians or official review by the Clay Mathematics Institute, a process that historically can take months or years. The flurry of AI-driven formalizations—other labs have reported rapid formal verification of classical results—has prompted discussion in the mathematics community about how quickly difficult problems are being consumed and how credit, review, and reproducibility should be handled as powerful models are applied to foundational research questions.