OpenAI's Astra Model Solves 10 Long-Standing Math Problems in Landmark AI Breakthrough

OpenAI has revealed that an internal version of its next major model, Astra, has produced solutions to ten long-standing open problems in mathematics and theoretical computer science — many of which had seen no significant progress for a decade or more.

The results, announced on August 1, 2026, come with a 249-page manuscript and fully machine-checkable Lean 4 certificates published on GitHub. Total compute cost for all ten solutions is estimated at roughly $2,000 at current Sol API rates.

What was solved

Among the headline results:

• The first explicit construction of a non-sofic group, resolving a central question in group theory that has stood since Mikhail Gromov introduced soficity in 1999.
• A disproof of Connes’s rigidity conjecture on von Neumann algebras.
• New upper bounds on high-dimensional sphere-packing density — the first general improvement since 1978.
• Resolution of three problems from Paul Erd?s’s catalogue, including a major advance on multicolour Ramsey numbers.
• New lower bounds on the circuit complexity of computing the permanent and hardness results relevant to post-quantum cryptography.

Why it matters

These are not benchmark scores or re-derivations of known results. They are genuine research-level mathematical advances generated by an AI system, then formalized into verifiable proofs. Mathematicians such as Thomas Bloom have called the constructions “big news.”

OpenAI researchers note that humans prepared the manuscripts with the model’s assistance, while Astra itself produced the core arguments and the Lean formalizations. The company is releasing reasoning walkthroughs for each solution so the community can inspect the work.

What comes next

If the proofs hold up under expert scrutiny, this marks one of the clearest demonstrations yet that frontier models can contribute original scientific knowledge rather than merely reorganize existing information. The $2,000 cost also shows that such breakthroughs are becoming economically accessible.

Astra remains unreleased. OpenAI has positioned it as its next major model family focused on long-horizon scientific reasoning.