OpenAI and the Hodge Conjecture

OpenAI employees expect to crack the Hodge Conjecture soon, according to a single source at OpenAI reported by The Information. OpenAI also confirmed to the New York Times that it made 'substantial progress' on a Millennium Prize problem within five days and was preparing to announce results. The Hodge Conjecture is described as 'arguably the most abstract of the seven Millennium Prize puzzles,' with five of the seven still unsolved. The model behind this work began training on August 28, 2026, after OpenAI paused frontier RL training from June 22. That model's mathematical capabilities significantly exceed GPT-6 Astra, and it solved the Navier-Stokes equations while still in training and not specifically aimed at mathematics. OpenAI engineers view dominating mathematics as a pathway to recursive self-improvement and see a business opportunity in doing for mathematics what large language models did for coding. OpenAI's earlier Navier-Stokes announcement angered the math community, sparking speculation that findings were lifted from other mathematicians. OpenAI has stated: 'We believe it is important to inform the world about the pace of AI progress and what to expect from upcoming models'. Outside sources suggest the new model's code name may be Aeon, though OpenAI has not confirmed this.