OpenAI Confirms Substantial Progress on Hodge Conjecture

OpenAI has confirmed to The New York Times that it has made substantial progress on the Hodge conjecture in the past five days, following its earlier breakthrough on the Navier-Stokes problem. The company is currently evaluating how to carefully release the results.

The Hodge conjecture, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute, carries a $1 million reward. Proposed by Scottish mathematician W. V. D. Hodge, it aims to bridge topology and algebraic geometry, asserting that certain topological holes in complex algebraic varieties are supported by algebraic equations.

In late August 2026, OpenAI completed training of a new internal model, which outsiders speculate is named Aeon. The model's mathematical reasoning ability is said to significantly surpass that of the previous strongest model, Astra. It reportedly solved the Navier-Stokes equation from scratch in just 88 hours.

Meanwhile, Anthropic is also reported to be close to solving the Birch and Swinnerton-Dyer conjecture. If these developments are confirmed, several long-standing Millennium Prize Problems could be cracked by AI within a month.