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

In brief

• OpenAI told the New York Times it has made "substantial progress" on a second Millennium Prize Problem since solving Navier-Stokes on September 8, without naming the problem or a disclosure timeline.
• Online speculation, unconfirmed by OpenAI, points to the Hodge Conjecture, a 76-year-old puzzle about counting the "holes" in complex geometric shapes.
• The Clay Mathematics Institute's review of OpenAI's Navier-Stokes proof is still pending, and a separate credit dispute with mathematician Tristan Buckmaster remains unresolved.

OpenAI isn't done cashing in on math's hardest open questions—at least not on the credit for solving them, since the company says it doesn't want the money.

Days after claiming a solution to the Navier-Stokes equations, OpenAI told the New York Times it has made "substantial progress" on another Millennium Prize Problem, one of seven grand puzzles the Clay Mathematics Institute has backed with a $1 million bounty since 2000.

OpenAI still hasn't said which problem it means, but experts, enthusiasts—and reporters—have their theories.

Chatter across social media has zeroed in on the Hodge Conjecture, a 1950 puzzle about how to count the "holes" in complex geometric shapes—the kind with so many dimensions nobody can actually picture them. Mathematician William Hodge proposed a shortcut using algebra instead of geometry to do it, but nobody has proven the shortcut always works.