Just weeks after claiming to have solved a 90-year-old Millennium Prize Problem that sparked outrage across the global mathematical community, OpenAI has published hundreds of new mathematical results produced by an internal frontier model. The Sam Altman-led lab released an open repository containing 722 research manuscripts organised into 372 distinct problem families. The documents cover a vast array of disciplines, including number theory and algebraic geometry, and claim major advances tied to three of the five remaining Millennium Prize Problems, including the legendary Riemann hypothesis.
The repository features 722 manuscripts across 372 families with each family group containing primary findings alongside companion arguments, corollaries and alternative proof strategies, according to OpenAI’s documentation. Alongside the raw papers, the lab published 10 breakdowns of the model’s internal reasoning chains, estimates of total compute expenditures, and aggregate statistics tracking the total volume of attempted problems. The company revealed that the average mathematical result consumed the compute equivalent of roughly three hours of ChatGPT Pro thinking time.
“We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results,” the company added. Behind closed doors, OpenAI continued running its models on open research challenges after standard mathematical benchmarks became saturated. OpenAI acknowledged that not every paper is completely verified or paired with computer-checked formal code, and to build trust, the company is publishing formalisations in Lean (a programming language designed to let computers verify proof logic) and promised to add more over time. OpenAI also conceded that unformalised results may contain errors, pledging to patch identified flaws quickly while exploring community-hosted repositories. In a bid to demonstrate scientific openness, OpenAI shared technical data detailing the resources required to generate the proofs.