OpenAI announced on August 1 that an internal version of Astra, its next major model family, produced solutions to ten open problems in mathematics and theoretical computer science, each unsolved for at least a decade. The headline result is the first explicit construction of a non-sofic group, closing a question left open since mathematician Mikhail Gromov introduced the concept in 1999. The model also disproved Connes's rigidity conjecture on von Neumann algebras, proved Ehrhart's volume conjecture, and resolved three Erdős problems, including one on multicolored Ramsey numbers.
Every result ships with a machine-checkable Lean 4 certificate, published on GitHub under an Apache 2.0 license alongside a 249-page manuscript. The repository reports a "sorry count" of zero, meaning no step in any of the ten formal proofs is left unverified — Lean's trusted kernel gives a binary compile-or-fail verdict that requires no advanced degree to check. OpenAI says the entire effort cost roughly $2,000 in compute at its GPT-5.6 Sol API rates.
Sebastien Bubeck, OpenAI's head of mathematics research, called the results "beautiful," and Fields Medalist Timothy Gowers said he would recommend one of the proofs for a top journal without hesitation. Thomas Bloom, who maintains the erdosproblems.com database, described the news as significant, drawing a contrast with OpenAI's October 2025 math claims that were later retracted. None of the ten results have yet undergone formal peer review, and OpenAI has given no release date, pricing, or API access details for Astra itself.