OpenAI Unveils Astra: A New Model Solving Ten Decades‑Old Math Problems

Yesterday OpenAI posted a seemingly modest mathematical announcement that actually introduced a previously unreleased model named Astra.

OpenAI describes Astra as its next‑generation primary model. In its first public appearance the model delivered ten new results on long‑standing open problems that have seen little progress for at least ten years.

The accompanying paper (https://cdn.openai.com/pdf/ten-proofs-oai.pdf) lists the ten problems: high‑dimensional sphere packing, binary and spherical coding, non‑sofic groups, the Connes rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, the nearest‑vector problem, the Ehrhart volume conjecture, multicolour Ramsey numbers, and extremal graph theory.

Key breakthroughs include the first explicit construction of a non‑sofic group, a refutation of the Connes rigidity conjecture, solutions to two Erdős problems, and new results directly relevant to post‑quantum cryptography. The coding‑theory section claims the first improvement in high‑dimensional exponents since 1977‑78.

OpenAI estimates the token cost of generating the ten proofs using Sol API pricing and states that the core mathematical reasoning was produced by Astra. Human collaborators organised the manuscript, after which Astra formalised each proof into Lean certificates that can be mechanically checked, and the model’s inference narratives for each solution were released.

A report by The Information adds that Sam Altman demonstrated Astra to policymakers in Washington. The model targets long‑duration tasks, enabling multiple agents to cooperate on complex projects and advanced mathematics, and may belong to a new class alongside Sol, Terra, and Luna.

The author emphasizes that Astra is not merely a more chatty ChatGPT; it is intended as a research collaborator capable of sustained exploration, orchestrating agents, and delivering conclusions to formal verification systems.

Overall, Astra shifts the focus from answering known questions to discovering new routes and allowing machines to participate in scientific discovery.

OpenAI 官方公告 https://openai.com/index/ten-advances-in-mathematics/
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