OpenAI has announced that its unreleased Astra model family has achieved significant progress on 10 long-standing mathematical problems. If independently verified, this breakthrough would represent a major evolution for artificial intelligence, positioning it as a legitimate contributor to scientific discovery.
According to OpenAI, the Astra model tackled problems across 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, which researchers then converted into formal manuscripts, verifying every logical step using the proof assistant Lean.
AI Expands Its Role in Scientific Discovery
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 such complex problems. The advances include breakthroughs 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.
This announcement builds on OpenAI’s earlier milestone in May 2026, when another unreleased AI model reportedly generated a disproof of the Erdős unit-distance conjecture, an open problem that had remained unsolved for more than 80 years.
Experts Call for Careful Evaluation
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 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.