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

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.

OpenAI hasn’t confirmed that guess, and it hasn’t confirmed rumors that the unreleased model behind the work is the rumored Aeon version built for long time horizon tasks and agentic workflows. Both are speculation, not company statements.

Back in September 8, OpenAI said an unreleased internal model produced a Lean-verified proof—Lean being software that checks a math proof one logical step at a time—showing the Navier-Stokes equations, which describe how fluids like air and water move, can “blow up” into a physically impossible infinite speed. Getting there took roughly 10,000 coordinating AI agents working for about 88 hours.

That’s a big deal beyond the math department. Navier-Stokes underpins aircraft design, weather forecasting, and how doctors model blood flow, and it had resisted a full mathematical explanation for nearly 90 years.

But the announcement landed messy. NYU mathematician Tristan Buckmaster laid out his side in a four-page statement: he and Anthropic researcher Levent Alpöge had quietly chased a related proof for almost a year and finished by August 22—before OpenAI’s Sébastien Bubeck learned about it and raced to publish first.

Buckmaster says Bubeck told him to either let OpenAI publish the day after his team or write it up alone, without Alpöge, since he works at a rival lab. “Why would you ruin your career?” Bubeck allegedly told him when he refused.

This new wave of AI models are so powerful they’re making math look cool. The same week, Anthropic said its Claude model formalized a 358-year-old proof of Fermat’s Last Theorem in 11 days, and mathematician Terence Tao warned that AI labs racing each other is burning through math’s supply of hard, useful problems faster than new ones can be found.

OpenAI says it isn’t chasing the $1 million prize for publishing any result—it’s using the problems as a public yardstick for how fast its models are improving. The next test of that yardstick is whether the Clay Institute, or any mathematician outside the company, can independently confirm even one of its claims—a process that, for past Millennium Prize submissions, has taken years rather than weeks.