Astra model reports ten advances across mathematics
OpenAI has released ten claimed advances in mathematics and theoretical computer science. The company says an internal version of Astra, described as its next major model, generated the mathematical arguments. People then prepared manuscripts with the same system, and the model formalized every argument as a Lean certificate.
The problems had reportedly seen no progress on their main result for at least a decade, and in most cases much longer. They range from high-dimensional geometry and coding theory to group theory, operator algebras, quantum complexity, lattice cryptography and extremal combinatorics.
What the ten results cover
The collection includes new bounds for high-dimensional sphere packing and binary and spherical codes. It also presents a construction of non-sofic groups, a disproof of Connes’s rigidity conjecture, and lower bounds for computing the permanent with arithmetic circuits and formulas.
Other results concern parallel repetition for two-player quantum games, approximation hardness for the closest vector problem and Ehrhart’s volume conjecture. OpenAI also reports a lower bound for multicolor triangle Ramsey numbers and results resolving two Erdős problems in extremal graph theory.
Cost, verification and responsibility
OpenAI estimates that finding all ten solutions would cost about $2,000 in tokens at Sol API rates. It separates the origin of the arguments from later editorial work: the system generated the mathematics, people helped prepare the papers, and the model produced formal Lean versions. Reasoning walkthroughs are being released with the manuscripts.
Formal certificates and published reasoning make scrutiny easier, but they do not replace independent review. Specialists still need to test definitions, assumptions, proof steps, novelty and links to existing literature. The broader signal is that AI is moving beyond summaries and routine calculation toward original, testable research contributions.
What changes for research teams
Institutions will need clear rules for attribution, reproducibility and expert verification when AI contributes arguments. OpenAI connects the release with ChatGPT for Academic Researchers, which offers 100,000 scientists and mathematicians free access to its strongest ChatGPT models. Access now has to grow alongside rigorous evaluation.