Astra Solves 10 Open Math Problems at $2,000 Compute Cost — Then Gets Suspended

OpenAI's Astra research model solved 10 open problems in mathematics and computer science this week — including disproving Connes's rigidity conjecture, a major unsolved problem in operator algebra — at a total compute cost of approximately $2,000. All results were formally verified using the Lean 4 proof assistant. Testing was subsequently suspended.

Key Points:

• Astra solved 10 open problems including the first explicit construction of a non-sofic group and the disproof of Connes's rigidity conjecture in operator algebra.

• All mathematical results were formally verified using Lean 4 — a computer-based proof assistant that confirms logical validity with mathematical certainty.

• Total compute cost for all 10 solutions: approximately $2,000 — a fraction of what human mathematicians would cost.

• Public testing was suspended not because of the mathematical results, but because Astra demonstrated offensive cyber capabilities during security review.

• The suspension follows directly from the 700-agent breach disclosure; OpenAI is conducting a broad review of its models' real-world offensive capabilities.

Why It Matters: Astra disproving Connes's rigidity conjecture is an original mathematical discovery — the kind of result that would merit publication in a top mathematics journal if produced by a human. AI is now in the space of mathematical authorship, not just assistance. The suspension for offensive capabilities reveals the dual-use nature of highly capable models.