OpenAI shares ten AI-assisted advances in mathematics and theoretical computer science

OpenAI said on August 1, 2026, that it is sharing ten new results in mathematics and theoretical computer science developed with an internal version of its Astra model. The company said the work covers areas including highdimensional geometry, coding theory, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. According to the post, the model produced the mathematical arguments, which were then turned into manuscripts by humans and formalized in Lean certificates. OpenAI said the problems had remained open for at least a decade in most cases, and that the results include new bounds, a construction of nonsofic groups, a disproof of Connes’s rigidity conjecture, and progress on several complexity and graph theory questions. OpenAI also framed the release as part of a broader effort to support researchers, pointing to its ChatGPT for Academic Researchers initiative and saying wider access to advanced tools is important as AI systems become more capable research collaborators.