OpenAI reveals Astra, an AI model that solved ten math problems mathematicians struggled with for decades

OpenAI has officially confirmed the existence of a new AI model, Astra, describing it as its 'next major model family'. An internal version of Astra helped solve ten open problems in mathematics and theoretical computer science that researchers had been working on unsuccessfully for at least ten years, and in some cases much longer. The solved problems include topics in high-dimensional geometry, coding theory, group theory, quantum complexity, lattice-based cryptography, and extremal combinatorics. Notably, Astra constructed the first example of a non-sofic group, an object whose existence had been discussed for many years. Mathematician Thomas Bloom of the University of Manchester called the results 'big news', noting they are more significant than the May counterexample to the unit distance conjecture, but he does not believe mathematicians will be replaced by AI soon, as AI systems are built on the long-term work of the mathematical community. Noam Brown, a reasoning technology developer at OpenAI, said the company has tried to apply Astra to other famous open problems but so far without success, and he wrote on X: 'Unfortunately, no Millennium Prize problems (yet).' The Clay Mathematics Institute pays $1 million for each of the seven Millennium Prize Problems, only one of which has been solved since 2000. OpenAI estimates that the computing required for all ten solutions would cost about $2,000 at current API rates for its Sol model. The researchers turned the ideas into full scientific papers, and all proofs were formalized in Lean, a system that combines a programming language and an interactive proof checker, providing machine-verified proofs. OpenAI has published step-by-step reasoning for each result, stressing that researchers are responsible for final publications but the mathematical ideas and proof logic came from Astra. Earlier, OpenAI said it was developing a new model family for long and complex tasks, and CEO Sam Altman introduced Astra to US government and regulatory officials, highlighting its ability to coordinate many AI agents. According to sources, Astra will join the Sol, Terra, and Luna model families, and its commercial name is unknown. OpenAI promised to publish a detailed technical report. New models are undergoing internal testing and will be the first to be evaluated under a US procedure for advanced AI models, with a key challenge being stable long-chain reasoning.