OpenAI named its next major model family Astra on Aug. 1 and said an internal version solved 10 long-open problems in math and theoretical computer science.
Key Points:
- OpenAI confirmed the Astra name in a report crediting the model with 10 results on problems untouched for at least a decade.
- The list includes a construction of non-sofic groups, a disproof of Connes's rigidity conjecture and three Erdős problems.
- Every argument shipped with a machine-checkable Lean certificate, and the token cost came to roughly $2,000 at Sol API rates.
OpenAI Astra Report Lists 10 Math Results
The company published a 249-page report on Saturday covering sphere packing, coding theory, arithmetic circuit complexity, group theory, quantum complexity and lattice cryptography.
Every problem on the list had gone at least a decade without progress on its main result, and most had stalled far longer. One construction establishes that non-sofic groups exist, settling a central question in group theory.
Other entries disprove Connes's rigidity conjecture, prove Ehrhart's volume conjecture and resolve three problems drawn from the Erdős catalogue, including a lower bound for multicolor triangle Ramsey numbers. OpenAI put the token cost of finding all 10 solutions at roughly $2,000 at Sol API rates.
Astra is built around multiple agents that split one hard task, work in parallel over long stretches and pool their results. The family sits beside the Sol, Terra and Luna models that carry the GPT-5.6 label. OpenAI has not decided whether it ships as GPT-6, as a GPT-5.7 variant or as a separate tier, and it has set no release date.
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Mathematicians Weigh Astra's Lean Proofs
Thomas Bloom, a University of Manchester mathematician who curates the Erdős problems catalogue, called the results "big news" on X. He rated them above the unit distance counterexample that OpenAI released in May, at least in terms of constructions.
Each argument arrives with a machine-checkable Lean certificate, a bar that few claims about AI research have cleared. Mathematicians still have to confirm that every formal statement captures the problem their field actually considered open. Noam Brown, who worked on the reasoning methods behind the system, wrote that the run cracked no Millennium Prize problems.
Sam Altman Pitched Astra In Washington
Sam Altman demonstrated Astra to senators and senior administration officials in closed-door Washington meetings days before the report landed.
He met Senators Raphael Warnock and Bernie Moreno on Wednesday, and his schedule also carried sessions with Mark Warner, Treasury Secretary Scott Bessent and Commerce Secretary Howard Lutnick.
Astra is expected to be the first model submitted under a planned federal pre-release review framework.
OpenAI took a similar route in May, when it announced an AI-generated disproof of the Erdős unit distance conjecture through a blog post rather than a journal. Mathematicians answered in June with the Leiden declaration, an International Mathematical Union-backed warning about proof by press release, which the company cited on Saturday.
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