OpenAI previews Astra by having it solve ten decades-old math problems for $2,000

OpenAI announced on August 2, 2026 that an internal version of its next major model, Astra, resolved ten long-standing open problems across mathematics and theoretical computer science. Each had remained unsolved for at least a decade, spanning high-dimensional geometry, group theory, quantum complexity, lattice cryptography, and extremal combinatorics.

What was actually solved

The headline result is the first explicit construction of a non-sofic group, resolving a question that has stood open since Mikhail Gromov introduced the concept of soficity in 1999. The batch also includes a disproof of Connes's rigidity conjecture on von Neumann algebras, a proof of Ehrhart's volume conjecture, and solutions to three problems from Paul Erdős's catalogue, including problem 183 on multicoloured Ramsey numbers.

Verification, not just claims

OpenAI published a 249-page manuscript alongside machine-checkable Lean 4 certificates for every result on GitHub — meaning the proofs can be independently verified by a proof assistant rather than taken on faith. The company put the total compute cost at roughly $2,000 at its Sol API rates, a figure that's drawn as much attention as the results themselves given the scale of the problems.

Thomas Bloom, who maintains the Erdős problems tracking site, called the results "big news," and OpenAI's head of mathematics research, Sebastien Bubeck, confirmed them publicly. For teams evaluating frontier models on reasoning rather than chat quality, this is one of the more concrete recent data points — an unreleased model, benchmarked against real unsolved research problems with independently checkable output, rather than a leaderboard score.

Source: Bleeping Computer, Forbes, The Decoder.