OpenAI's Astra Model Solves Ten Decades-Old Math Problems

OpenAI disclosed an internal version of its next‑generation model, code‑named Astra, that produced solutions to ten long‑standing problems in mathematics and theoretical computer science. The breakthroughs span high‑dimensional geometry, coding theory, non‑sofic group existence, a refutation of Connes’s rigidity conjecture, quantum parallel repetition, lattice‑based cryptography, and several Erdős‑posed conjectures. OpenAI estimates the total token usage for the ten solutions would cost about US$2,000 at Sol API rates.

The company released a 249‑page manuscript and Lean 4 certificates for each proof, making the results machine‑checkable on GitHub under an open‑source license. Human researchers guided Astra’s reasoning, drafted the papers, and then had the model formalize the arguments in Lean. Astra was demonstrated to U.S. policymakers, and its capabilities may be subject to upcoming AI model review regulations. The model’s final commercial name remains undecided, with possibilities ranging from GPT‑5.7 to GPT‑6.