Mathematicians doubt report that OpenAI is close to the Hodge conjecture
The Information cited a person with knowledge of the work. Elliot Glazer says progress on a special case is likely, and a full solution this month is not.
OpenAI is close to solving the Hodge conjecture, one of the seven Millennium Prize Problems, The Information reported on Saturday, citing a person with knowledge of the work. The claim follows an Odd Lots interview in which Greg Brockman acknowledged significant progress on another such problem after the Navier-Stokes work. He did not say which problem.
Elliot Glazer, who has offered public wagers on the question, disputed the report's reach on Sunday. His view is that OpenAI may have made significant progress on a special case, Hodge for abelian varieties. That gives little reason to expect a full solution soon, he says. He put his confidence that a Millennium problem falls this month at 1 percent, down from 10.
Glazer said the report's source added two things to the public record. The problem is Hodge, and the lab is close to the full result. He strongly doubts the second. OpenAI would not leak progress over weeks if its team thought the full result was in reach, he argued, given the risk of Anthropic scooping it.
Another poster, Obhishek Saha, wrote that there is no chance OpenAI has proved the conjecture in general. A proof for all abelian varieties would still count among the best results produced by language models so far, he added. Prediction markets put the odds of a Millennium problem falling this year at 58 percent, according to one account.