OpenAI’s Astra Model Solves 10 Long-Standing Math and CS Problems

OpenAI has announced that an internal, unreleased model named Astra has solved 10 long-standing open problems in mathematics and theoretical computer science. The breakthrough signals a shift in AI capabilities from solving curated benchmarks to conducting original scientific research.

To validate the claims, OpenAI released a 249-page collection of manuscripts and reasoning walkthroughs via a public GitHub repository. Crucially, the company provided machine-verifiable Lean certificates for every solution, allowing the mathematical correctness to be mechanically confirmed by a computer rather than relying on trust in the lab. According to OpenAI, the Astra model generated the underlying arguments, while human researchers assisted in preparing the final manuscripts and formalizing the proofs within the Lean language.

A Broad Spectrum of Discovery

The 10 solved problems span several complex domains of theoretical study. These include high-dimensional sphere packing, binary and spherical codes, non-sofic groups, and Connes's rigidity conjecture. The model also addressed arithmetic circuit complexity, quantum parallel repetition, the closest vector problem, and Ehrhart's volume conjecture. Additionally, Astra solved problems regarding multicolor Ramsey numbers and two specific conjectures in extremal graph theory.

This development follows a broader trend of frontier AI labs moving toward original discovery. This latest effort positions the next generation of models as research infrastructure, competing with other high-reasoning systems. By moving beyond static datasets, these models are beginning to function as active collaborators in the pursuit of mathematical truth.

The End of Probabilistic Guessing

The ability to produce machine-verifiable proofs marks a critical transition from "probabilistic guessing" to rigorous reasoning. By utilizing Lean certificates, OpenAI addresses the persistent problem of AI hallucinations in mathematics, where models often produce plausible-sounding but incorrect proofs.

Beyond the theoretical victory, the economic efficiency of the discovery is notable. OpenAI estimates that the tokens used to find these 10 solutions cost approximately $2,000, based on GPT-5.6 Sol API rates. Given that these problems have resisted human effort for decades, the low cost of compute suggests that AI-assisted research could drastically accelerate discovery in high-stakes fields, including quantum complexity theory and post-quantum cryptography via the closest vector problem.

What Comes Next

Despite the results, the Astra model remains internal and has not been released to the public; the current announcement serves as a capability preview. The internal nature of the model suggests OpenAI is carefully calibrating the system's safety and reliability before a wider rollout.

Industry observers will now be watching to see if OpenAI opens the model to the wider academic community or keeps it as a proprietary tool for internal research. The primary remaining question is whether this capability can be generalized across other hard sciences, such as physics or chemistry, where formal verification tools like Lean are less prevalent. If such a transition is possible, it could redefine the methodology of scientific inquiry across the board.