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OpenAI Astra disproved Connes’ Rigidity Conjecture — and 9 other decades-old math problems, each with a Lean certificate

On August 1 OpenAI published “Ten advances in mathematics and theoretical computer science,” and dropped the name of its next flagship: Astra. This isn’t a chatbot. Astra is a multi-agent, long-horizon model — many agents grinding on a single problem for hours, sometimes days.

What it actually did

Ten problems that had sat open for a decade or more. A disproof of Connes’ Rigidity Conjecture in von Neumann algebras. A construction of non-sofic groups. Tighter high-dimensional sphere-packing bounds pushing toward the Cohn–Elkies limit. Circuit complexity, monochromatic triangles in colored graphs, and more. Sébastien Bubeck is posting them one by one on X. Total compute to find all of it: roughly $2,000 in tokens.

Why the Lean certificates matter

You don’t have to trust Astra. Every proof ships with a full Lean formalization certificate plus a chain-of-thought walkthrough — machine-checkable, line by line. That’s the whole point: AI research output you can verify instead of vibe-check.

Altman already demoed Astra to regulators in Washington. The name isn’t final — GPT-6, GPT-5.7, or its own series — and there’s no launch date yet.


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