OpenAI's Astra Cracks 10 Decade-Old Math Problems, Including First-Ever Non-Sofic Group

Summary: OpenAI's unreleased Astra model independently solved ten open problems spanning group theory, lattice cryptography, coding theory, and combinatorics — releasing Lean 4 machine-verified certificates and a 249-page manuscript on GitHub.

Key facts

• Headline result: the first explicit construction of a non-sofic group, resolving a central question in group theory open since Mikhail Gromov introduced the soficity concept in 1999.
• Results span high-dimensional geometry, arithmetic circuit complexity, quantum complexity, and extremal combinatorics — none had seen core progress for at least a decade.
• Lean 4 formal proofs accompany every result, making the work machine-checkable rather than relying on peer trust alone.
• Total compute cost to find all ten solutions: roughly $2,000 at Sol API rates. Astra remains unreleased, with no timeline or naming decision announced.

Why it matters

This marks the clearest demonstration yet of AI moving from accelerating existing research to independently advancing the mathematical frontier. Fields Medalist Timothy Gowers said he would recommend one of the proofs for a top journal without hesitation — a bar that pure AI output had not previously cleared at this scale.

Read more

• Ten advances in mathematics and theoretical computer science — OpenAI
• OpenAI teases Astra after solving 10 math problems — BleepingComputer