---
answer: direct
beat: ai-technology
source: 1 article · updated: August 6, 2026
---

What open math problems did OpenAI's Astra model solve?

Astra solved ten longstanding open problems, including constructing a non-sofic group (open since 1999), disproving Connes's rigidity conjecture on von Neumann algebras, proving Ehrhart's volume conjecture, and resolving three problems from Paul Erdos's catalog including problem 183 on multicolor Ramsey numbers.

Answered in

OpenAI's Astra Model Solved 10 Open Math Problems — With Machine-Verified Proofs

OpenAI's Astra solved 10 longstanding open math problems with fully verified Lean 4 proofs and zero unproven steps. Total compute cost: roughly $2,000.

Crashtech Editorial August 6, 2026 How AI Actually Works

Read the full analysis

Other questions this article answers

More how ai actually works questions

Every answer on Crashtech is written by the editor of the article it comes from — never auto-summarised. Browse all answers or the How AI Actually Works beat.