OpenAI claims that an in-house version of its next model has settled ten open questions for at least a decade, producing machine-verifiable evidence.
On August 1, 2026, OpenAI announced that an internal version of its next model, called Astra, had solved ten mathematical problems that had remained open for at least a decade. The fields concerned range from group theory to large-scale geometry and quantum complexity. The advanced calculation cost is approximately $2,000.
Particularity of the announcement: each demonstration is formalized in Lean 4 and published on GitHub under Apache 2.0 license. So any researcher can run the evidence checker without having to believe OpenAI on word — a break with previous sector announcements, often unverifiable.
Among the results put forward are the explicit construction of a non-sofic group, a question left open since Mikhail Gromov formulated the concept of solicity in 1999, the refutation of Connes's rigidity conjecture on von Neumann's algebras, and the resolution of three problems in Paul Erdős' catalogue. None of these ten results have yet been peer reviewed, which calls for caution in their actual scope.
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