OpenAI names its next model by handing in homework: ten open problems, proofs checked by machine, $2,000 of compute

OpenAI has revealed the name of its next major model, Astra, in an unusual way: not with a benchmark table, but with a 249-page manuscript claiming solutions to ten problems that mathematicians had failed to crack for at least a decade each. The list ranges across high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, quantum complexity, lattice cryptography and extremal combinatorics. The headline item is an explicit construction of a non-sofic group — a question left open since Mikhail Gromov introduced soficity in 1999. The manuscript also reports a disproof of Connes's rigidity conjecture, a proof of Ehrhart's volume conjecture, and answers to three problems from Paul Erdős's catalogue. What makes the claim unusually checkable is that every proof was formalised in Lean 4 and published, with the certificates on GitHub under an Apache-2.0 licence. In Lean, an unfinished step has to be marked with the keyword "sorry"; the repository's count of those is zero, which means the proofs verify end to end without a human being asked to take anything on trust. The compute bill for generating all ten solutions came to roughly 2,000 dollars at OpenAI's own API rates. Astra itself is not a product. OpenAI describes it as a model family built for tasks that run for hours or days with several agents working in parallel, and says it has not decided whether it ships as GPT-6 or as a variant of the GPT-5 line. No weights, no pricing, no context window and no release date have been published, and Sam Altman has so far shown it to policymakers in Washington rather than to customers. Mathematicians have been enthusiastic but precise about what happened. Thomas Bloom of the University of Manchester called the results big news and clearly more significant than the model's results in May, while rejecting the framing that mathematicians are being replaced: the machine worked inside a century of human theory rather than around it. We are not opening a catalogue profile for Astra until OpenAI publishes an actual model card.