According to a recent report by The Information, employees inside OpenAI expect the company to soon notch a breakthrough on another Millennium Prize Problem, reportedly targeting the famous Hodge Conjecture. OpenAI has not publicly confirmed the news.
The Hodge Conjecture is one of seven Millennium Prize Problems designated by the Clay Mathematics Institute. Its core question concerns the topological features of the solution sets of algebraic equations and whether those features can be described by lower-dimensional algebraic-geometric objects. The Clay Mathematics Institute still lists it as unsolved and has set a US$1 million prize for each Millennium Problem.
OpenAI is closing in on the Hodge Conjecture
According to information obtained by CNMO Tech, OpenAI has once again drawn outside attention, this time in connection with the earlier Navier–Stokes problem. On September 8, OpenAI published a claimed solution to the Navier–Stokes existence and smoothness problem, saying the work had been carried out by its in-house AI system and accompanied by a Lean formal proof. OpenAI said the result was primarily intended to showcase its AI model's capabilities and that it had no plans to apply for a Millennium Prize.
The announcement quickly drew pushback from mathematicians. Some questioned the timing of OpenAI's disclosure, the way the research collaboration was conducted, and whether OpenAI's team might have had access to work already produced by other researchers. New York University mathematician Tristan Buckmaster noted that he and Anthropic researcher Lev Antopol had already completed a related proof as early as August 22, and he suspected that OpenAI's model may have "peeked at" an unpublished draft he had stored in an OpenAI coding tool.
Against that backdrop, The Information reported that OpenAI employees expect the company to be closing in on a second Millennium Prize Problem. A follow-up disclosure, however, showed that OpenAI only confirmed to The New York Times that it had made "significant progress" on another Millennium Prize Problem, without specifying which one. As a result, the Hodge Conjecture cannot yet be treated as officially confirmed.
The Information also reported that OpenAI engineers view mathematical reasoning as a key avenue for further improving AI capabilities, and that tackling high-difficulty math problems may be tied to recursive self-improvement (RSI).