OpenAI announced that an internal version of Astra, its upcoming major model family, produced verified solutions to 10 previously unsolved problems spanning geometry, group theory, quantum complexity, and theoretical computer science. Some of these problems had remained open for nearly three decades.
The Breakthrough Results
The headline achievement is the first explicit construction of a non-sofic group, resolving a central question in group theory that mathematician Mikhail Gromov posed in 1999. For 27 years, no mathematician had managed to prove or disprove whether such groups exist. Astra also disproved Connes's rigidity conjecture on von Neumann algebras, proved Ehrhart's volume conjecture, and cleared three problems from Paul Erdős's famous list that had seen no progress in over a decade.
OpenAI published a 249-page manuscript collection alongside machine-checkable Lean 4 certificates for all 10 results on GitHub under an Apache 2.0 license. The repository reports zero "sorry" counts, meaning no proof step was left unverified. The total token cost for generating all solutions came to roughly $2,000 at Sol API rates—a price point that could democratize access to frontier mathematical research if the model were publicly available.
The Catch
None of the 10 results has undergone traditional peer review yet. While the Lean certificates provide binary verification that the proofs compile, mathematicians still need to confirm that each formal statement correctly captures what the original problem asked and judge whether the results matter. OpenAI is also giving 100,000 academic researchers free access to its frontier models through 2027, deepening its ties to scientific institutions while concentrating research infrastructure on its closed platform.