OpenAI has announced its next major model family, Astra, which has solved ten previously unsolved math problems. The results cover multiple fields, including high-dimensional geometry and group theory. The company said an internal version of Astra solved these problems, which mathematicians had made no progress on for at least a decade. OpenAI released a math report confirming the Astra name and detailing the solutions.
The models are currently being tested and will be the first to go through a planned U.S. government review process before public release. OpenAI stressed the system's ability to coordinate multiple agents over extended periods to tackle especially hard problems. The company pointed to complex projects and advanced math as potential use cases. Astra's solutions would cost about $2,000 at API rates, according to the report.
OpenAI said the tokens used to generate all ten solutions would have cost about $2,000 at Sol's API rates. After the model produced its arguments, humans worked with the same model to turn them into research papers. The model also formalized each proof in Lean, creating machine-checkable certificates of mathematical correctness, and OpenAI published a walkthrough of the model's reasoning process for each solution. OpenAI said its researchers helped prepare the papers and formalize the proofs, and that the company takes responsibility for their accuracy.
The mathematical arguments themselves, however, came from Astra. The company argued that claiming human authorship for a proof generated entirely by AI would misrepresent both the system's contribution and the nature of genuine human intellectual work, pointing to the Leiden Declaration on AI and Mathematics as a reference for how credit should be assigned in AI-assisted research. Source: thedecoder
