OpenAI AI model achieves a mathematical breakthrough: releases research results on 10 long-standing unsolved problems in cryptography, quantum computing, and more

According to official news, OpenAI has released research results stating that its next-generation AI model Astra has made progress in the fields of mathematics and theoretical computer science, involving areas such as high-dimensional geometry, coding theory, group theory, quantum complexity, post-quantum cryptography, and extremal combinatorial mathematics. The 10 published results include: the high-dimensional sphere packing problem, binary and spherical coding problems, non-sofic group problems, Connes rigidity conjecture, arithmetic circuit complexity problems, quantum parallel repetition problems, nearest vector problems, Ehrhart volume conjecture, multi-color Ramsey number problems, and extremal graph theory conjectures.

It is reported that these results were derived using an internal version of the Astra model, with the computational cost of finding solutions amounting to approximately $2000 (calculated based on Sol API prices).

Subsequently, human researchers used the same model to assist in compiling the results into a paper and generated verifiable proof certificates through the Lean formal proof system.