OpenAI announced that its unreleased Astra model family made major progress on 10 long-standing mathematical problems. Independent verification would confirm a major evolution, positioning AI as a legitimate contributor to scientific discovery.
According to OpenAI, the unreleased Astra model worked across several advanced mathematical fields, including high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. The company said the AI generated the mathematical arguments, while researchers later converted them into formal manuscripts and verified every logical step using the proof assistant Lean.
OpenAI revealed that producing the solutions required computing resources worth approximately $2,000 at GPT-5.6 Sol API rates, indicating relatively efficient reasoning for problems of such complexity.
According to the company, Astra generated advances in sphere packing, error-correcting codes, the construction of the first explicit non-sofic group, and new results related to Ehrhart's volume conjecture, Connes' rigidity conjecture, and the quantum parallel repetition theorem.
The announcement builds on OpenAI's earlier research milestone in May 2026, when another unreleased AI model reportedly generated a disproof of the Erdős unit-distance conjecture, an open mathematical problem that had remained unsolved for more than 80 years.
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Researchers are urging caution pending independent verification and peer review. The Leiden Declaration on AI and Mathematics, published in June 2026 and signed by hundreds of mathematicians, flagged concerns about unreliable AI-generated proofs, attribution, disclosure, and research bias.
Commenting on the debate, mathematician Kevin Buzzard of Imperial College London said, "Mathematicians should find it quite striking that tech companies are suddenly interested in their work. The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space."
OpenAI acknowledged these concerns, stating, "There are many views as to the role of AI in mathematics, and we have deep respect and understanding for those concerned with its impact." The company also said it plans to publish Astra's reasoning process and recently launched ChatGPT for Academic Researchers, giving 100,000 scientists and mathematicians free access to its latest AI models to support future research.