OpenAI says AI system advances 10 major math problems

OpenAI has announced that an internal version of its upcoming artificial intelligence model, Astra, has achieved significant breakthroughs by solving or advancing 10 longstanding open problems in mathematics and theoretical computer science. According to the company, each problem had remained unresolved for at least a decade, with several challenging researchers for much longer. The discoveries span a wide range of advanced fields, including high-dimensional geometry, coding theory, group theory, quantum computing, lattice cryptography, operator algebras, and extremal combinatorics.

OpenAI said Astra produced new mathematical arguments that improve existing theoretical bounds, resolve multiple famous conjectures, and answer several problems originally posed by legendary mathematician Paul Erdős. Among the reported achievements are improved sphere-packing limits, stronger bounds for binary error-correcting codes, the construction of non-sofic groups, and a disproof of Connes' rigidity conjecture. The model also generated new results in arithmetic circuit complexity, quantum game theory, post-quantum cryptography, Ramsey theory, and extremal graph theory, demonstrating its ability to tackle some of mathematics' most difficult unsolved questions.

OpenAI stated that human researchers collaborated with the AI by organizing its discoveries into formal research papers and converting the proofs into Lean, a proof-verification system that enables machine-checkable mathematical validation. The company plans to publicly release explanations of the model's reasoning, allowing mathematicians to independently examine, verify, and build upon the findings. OpenAI emphasized that the mathematical arguments themselves were generated by the AI, while human researchers focused on documentation and formal verification.

The announcement highlights the growing role of artificial intelligence as a research collaborator capable of contributing beyond traditional tasks such as writing, coding, and data analysis. At the same time, OpenAI acknowledged that AI-generated discoveries raise important questions about authorship, academic credit, and the future relationship between human researchers and intelligent machines. The company argued that scientific attribution should accurately recognize AI contributions while maintaining transparency about human involvement.

By tackling problems that have resisted progress for decades, Astra represents OpenAI's latest effort to demonstrate that advanced AI systems can accelerate scientific discovery and expand the frontiers of mathematical research. Whether these breakthroughs withstand independent peer review, they signal a future in which mathematicians and AI systems increasingly work together to solve some of science's most complex challenges.