Ten Open Problems Tackled by an Internal Version of Astra

An internal version of Astra, OpenAI’s next major model, delivers ten advances on math problems left open for at least a decade.

An internal version of Astra, described as OpenAI’s next major model, has produced ten results on problems that had seen no major progress for at least a decade. The work spans high-dimensional geometry, coding theory, group theory, arithmetic circuits, quantum complexity, lattice-based cryptography, and extremal combinatorics.

The cited contributions include new bounds for sphere packing and binary codes, a construction of non-sofic groups, a disproof of Connes’ rigidity conjecture, and new results on the complexity of the permanent. The model is also said to have solved several Erdős problems, established a parallel repetition property for quantum games, and improved hardness results associated with the Closest Vector Problem.

OpenAI states that the mathematical arguments were generated by Astra and then turned into papers by human teams assisted by the same model. Each proof was subsequently formalized as a Lean certificate to verify the logical consistency of the individual steps. For each result, the company is also publishing a model-generated reconstruction of its problem-solving process.

According to OpenAI’s estimate, the total compute required to search for these solutions would amount to approximately $2,000 at GPT-5.6 Sol API pricing. The company notes that humans handled manuscript preparation and final verification, while attributing the production of the mathematical arguments to the system.

This publication follows an earlier AI-generated result concerning the Erdős unit-distance conjecture, as well as the ChatGPT for Academic Researchers program, which is expected to provide 100,000 researchers with free access to the company’s models.