OpenAI announces its “next major model” Astra by dropping ten previously unsolved math solutions

OpenAI has released its math report, officially confirming the Astra name for the first time. The company says an internal version of Astra, its “next major model family,” solved ten open problems in math and theoretical computer science.

Mathematicians had made no progress on any of them for at least a decade, and much longer in most cases. The results cover fields ranging from high-dimensional geometry and coding theory to group theory, quantum complexity, lattice cryptography, and extremal combinatorics. One proof establishes the existence of non-sofic groups, resolving a major open question in group theory.Ad Thomas Bloom, a University of Manchester mathematician who runs erdosproblems.com, called the results “big news” on X. He considers them more significant than the counterexample to the unit distance conjecture published in May. “Maybe not bigger than a proof of unit distance would have been, but in terms of constructions, this is big,” Bloom wrote.AdDEC_D_Incontent-1 Bloom also rejected the idea that AI is replacing mathematicians, arguing that the claim makes little sense when the AI draws on more than a century of mathematical theory, was built by mathematicians, and was trained on everything mathematicians have ever written. Noam Brown, one of the researchers behind the test-time reasoning technology used by Astra, said on X that OpenAI had also tried and failed to crack other major problems. “Sadly, no Millennium Prize Problems (yet),” he wrote. The Clay Mathematics Institute offers $1 million for solving each of the seven Millennium Prize Problems, but only one has been solved since the prizes were announced in 2000. Brown added, “But also, we didn’t spend a lot on each problem. It’s possible to push test-time compute much further.” He called Astra a “major step for scientific reasoning.”Ad Astra’s solutions would cost about $2,000 at API rates OpenAI says 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.AdDEC_D_Incontent-2 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.Ad OpenAI is reportedly building Astra, a model family designed to work on problems for hours or days OpenAI is working on a new model family tentatively called “Astra” that’s meant to be far more capable at long-running tasks than anything the company has shipped so far. CEO Sam Altman demoed Astra to politicians and regulators in Washington, D.C., this week.