OpenAI's Astra solves 10 long-open math problems and publishes the proofs

OpenAI Group PBC announced Saturday that an internal version of its Astra model family produced new results for 10 problems in mathematics and theoretical computer science that had been open for at least a decade and published machine-checkable proofs alongside the claim. The company posted a 249-page manuscript collection, model-written reasoning walkthroughs and Lean 4 certificates for all 10 results. The certificates sit on GitHub under an Apache 2.0 license, and the repository reports a "sorry" count of zero, meaning no step in any of the formalized proofs has been left unproven. The headline result is an explicit construction of a non-sofic group, a question left open since Mikhail Gromov introduced soficity in 1999. Astra also disproved Connes's rigidity conjecture and proved Ehrhart's volume conjecture. Three problems from Paul Erdos's catalog fell as well, including problem 183 on multicolor Ramsey numbers. Thomas Bloom, who maintains the erdosproblems.com database, called the Astra results "big news" and rated them ahead of the Erdos unit distance counterexample an internal OpenAI model produced in May. Astra itself remains unreleased. OpenAI describes it as a model family built to run long tasks by coordinating multiple agents over extended periods. Human researchers turned the model's output into publishable papers, though OpenAI said the mathematical arguments themselves came from Astra. None of the 10 results has been through peer review. The International Mathematical Union endorsed the Leiden Declaration in June, which warns that AI companies are using published research without consent, bypassing peer review, and threatening the integrity of proof and attribution.