OpenAI says Astra produced ten advances in mathematics

OpenAI published a collection of ten claimed advances in mathematics and theoretical computer science on August 1. The accompanying manuscript runs to 249 pages and addresses problems whose main results had remained open for at least a decade. OpenAI says the mathematical arguments were generated by an internal version of Astra, which it describes as its next major model.

The subjects range from high-dimensional geometry and coding theory to group theory, operator algebras, quantum complexity, cryptography and extremal combinatorics. Results include a construction of a non-sofic group, a disproof of Connes’s rigidity conjecture, improved bounds for sphere packing and codes, and a quantum parallel repetition theorem. The collection also includes a hardness result for the closest vector problem, which is relevant to post-quantum cryptography, and resolutions of three problems associated with Paul Erdős.

This is more ambitious than a conventional model benchmark. OpenAI says the total tokens used to find the solutions would cost roughly $2,000 at current Sol API rates. That comparison gives a sense of inference cost, but Astra itself is internal, so independent researchers cannot yet reproduce the same workflow through a public model.

OpenAI released more than summaries. It published the full arguments, a separate set of discovery notes and Lean certificates for every result. Lean formalisation can let software verify that a proof follows explicitly stated logical rules, reducing certain kinds of hidden error. It does not by itself establish a result’s importance, check every informal assumption around its framing or replace assessment by specialists. The mathematical community will still need to examine the proofs, definitions and relationship to earlier work.

The attribution is notable too. OpenAI says the system produced the mathematical arguments, while humans helped prepare the manuscripts with the model; Astra then formalised each proof in Lean. The company argues that presenting fully AI-generated arguments as human work would misrepresent how the results were obtained. That puts credit, responsibility and access at the centre of the discussion, alongside technical correctness.

For AI users and research organisations, the practical signal is that advanced models may be moving from solving set exercises toward proposing original research paths. The stronger lesson is methodological: consequential scientific claims need inspectable evidence, formal checks where possible and independent expert review. If the ten results hold up, the immediate change is not automated mathematics, but a much shorter loop between conjecture, proof, verification and further discovery.