OpenAI's AI model achieved a mathematical breakthrough: research results on 10 long-standing unsolved problems such as cryptography and quantum computing were released

Comparatively, OpenAI released research results saying that its next-generation AI model, Astra, has made progress in the fields of mathematics and theoretical computer science, involving high-dimensional geometry, coding theory, group theory, quantum complexity, post-quantum cryptography, and extreme value combinatorial mathematics. The 10 published results include: high-dimensional sphere accumulation problems, binary and spherical coding problems, non-sofic group problems, Connes rigidity conjecture, arithmetic circuit complexity problems, quantum parallel repetition problems, recent vector problems, and Ehrhart volume conjecture , multicolor Ramsey number problem, extreme value graph theory conjecture.

According to reports, these results were derived from the completion of an internal version of the Astra model, and the computational cost of finding a solution was approximately $2,000 (based on the Sol API price). Human researchers then used the same model to help organize papers and generate verifiable proof certificates through a lean formal proof system.