OpenAI reportedly close to solving Hodge conjecture, its second Millennium Prize Problem
OpenAI is said to be nearing a solution to the Hodge conjecture, the second of the seven Millennium Prize Problems, after an unconfirmed claim of solving the Navier‑Stokes problem. A person familiar with internal discussions told The Decoder that employees expect a breakthrough soon, though the company may hold off on any public announcement to avoid repeating the PR fallout from the…
Key points
- OpenAI is said to be near a solution to the Hodge conjecture, its second Millennium Prize problem.
- Employees expect a solution soon, but any announcement may be delayed after the Navier‑Stokes PR crisis.
- The effort uses a variant of the upcoming model codenamed “Doug,” reportedly costing millions of dollars.
The work reportedly builds on a variant of OpenAI’s next‑generation pretrained model, codenamed “Doug,” which the firm allegedly spent millions of dollars to develop. Chief researcher Jakub Pachocki had earlier indicated that the company’s primary focus was recursive self‑improvement rather than pure mathematics, but some insiders think a formal proof could feed into that agenda. Mathematicians, meanwhile, have expressed frustration and concern that AI breakthroughs could threaten traditional research approaches.
OpenAI reportedly closes in on solving the Hodge conjecture, its second Millennium Prize Problem
The Decoder · 17 September 2026
OpenAI reportedly closes in on solving the Hodge conjecture, its second Millennium Prize Problem
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.
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