# OpenAI's Astra solves 10 long-unsolved math problems, publishes verified proofs

> OpenAI says its next-generation system, Astra, cracked ten mathematics and theoretical computer science problems that had resisted proof for a decade or more. The headline result is an explicit construction of a non-sofic group, a question left open since 1999, alongside progress on Connes's rigidity conjecture, Ehrhart's volume conjecture, and three separate Erdos problems. What makes the claim hard to wave away is how it was published. Every proof went out in Lean 4, a formal proof language, with a reported 'sorry' count of zero, meaning a machine checked each step and found no gaps left to fill by hand. The company also pegs the compute bill at roughly two thousand dollars at current rates, a striking figure for work that would occupy specialists for months. If it holds up under scrutiny from working mathematicians, this is a different kind of milestone than a benchmark score. It suggests AI can now contribute verifiable, novel results at the frontier of pure math, not just reproduce known ones, and it hands the community proofs it can actually audit.

_Section: [Daily AI Updates](https://www.wortins.com/daily-ai) · Source: SiliconANGLE · Published Wednesday, August 26, 2026_

## Wortins' read

OpenAI says its next-generation system, Astra, cracked ten mathematics and theoretical computer science problems that had resisted proof for a decade or more. The headline result is an explicit construction of a non-sofic group, a question left open since 1999, alongside progress on Connes's rigidity conjecture, Ehrhart's volume conjecture, and three separate Erdos problems. What makes the claim hard to wave away is how it was published. Every proof went out in Lean 4, a formal proof language, with a reported 'sorry' count of zero, meaning a machine checked each step and found no gaps left to fill by hand. The company also pegs the compute bill at roughly two thousand dollars at current rates, a striking figure for work that would occupy specialists for months. If it holds up under scrutiny from working mathematicians, this is a different kind of milestone than a benchmark score. It suggests AI can now contribute verifiable, novel results at the frontier of pure math, not just reproduce known ones, and it hands the community proofs it can actually audit.

## Source

[Read the full story at SiliconANGLE](https://siliconangle.com/2026/08/02/openais-astra-solves-10-long-open-math-problems-publishes-proofs/)

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