OpenAI publishes 722 AI-generated math discoveries in major scientific milestone

OpenAI has put 722 math papers online that were generated by an unreleased AI model, and the batch spans about 20 subfields. The papers went up on GitHub late Tuesday. Some settle long-running hypotheses. Others knock down proposed explanations or narrow the field of possible answers to problems that still don’t have one.

The headline grabber is the Riemann hypothesis, a 150-plus-year-old problem tied to prime numbers. OpenAI’s model did not solve it outright. But it did prove an important related result, the quasi-Riemann hypothesis, which is a real step in a problem many mathematicians treat as one of the field’s great prizes. That matters because a lot of later work assumes the Riemann hypothesis is true; proving pieces around it helps sort out what stands and what doesn’t.

The company also leaned hard into theoretical computer science, with more than 80 papers in that area. Three of them focus on matrix multiplication, the kind of calculation AI systems use constantly when processing data. For decades, researchers have chased faster and more hardware-efficient ways to do it, with the belief that the gains eventually hit a ceiling. OpenAI’s model sharpened the definition of that limit. In another paper, it came up with a new way to multiply integers, another basic building block that software depends on.

There’s also a physics angle here. OpenAI published more than a dozen proofs connected to partial differential equations, the equations behind chip design, architecture, quantum mechanics and more. The model proved a version of De Giorgi’s conjecture, which is linked to an equation used to study metal alloys. It also clarified questions around the Navier–Stokes equations, which engineers use to study how liquids flow. In September, the same model solved a separate Navier–Stokes problem that ranked among the hardest open questions in mathematics.

OpenAI says many of the new papers include Lean files, so the proofs can be checked by computer. It plans to release Lean proofs for more of the papers and to help fund research events and programs focused on reviewing AI-generated math discoveries. That last part may be the most interesting: not just an AI writing proofs, but a pipeline for making humans verify them.