OpenAI is reportedly close to solving another of math's seven famous Millennium Prize Problems. After its still officially unconfirmed solution to the Navier-Stokes problem, the company is now working on the Hodge conjecture, which asks whether certain geometric properties of shapes can always be described through simpler algebraic building blocks. Employees expect a solution soon, according to a person familiar with the matter. Any announcement could be delayed, though. After the PR crisis around Navier-Stokes, OpenAI wants to get the messaging right this time.

For the Navier-Stokes solution, OpenAI used a variant of its next pretrained model, codenamed "Doug," likely at a cost of millions of dollars. Chief researcher Jakub Pachocki had said at the Astra launch that OpenAI would focus on recursive self-improvement first, meaning AI that optimizes itself, rather than math. What the company hopes to gain from solving these problems is unclear. Some inside OpenAI apparently believe it could feed into recursive self-improvement. The math community, meanwhile, is more angry than impressed. Some mathematicians see their entire field under threat.