OpenAI's Unreleased 'Astra' Model Cracks 10 Long-Open Math Problems — With Machine-Checkable Proofs
An internal OpenAI system reportedly produced verified Lean 4 certificates for a decade-old cluster of unsolved problems, including a non-sofic group construction and several Erdős conjectures, at a search cost of roughly $2,000 each.
OpenAI's unreleased model, referred to as Astra, has reportedly solved ten long-open problems in mathematics and theoretical computer science, and — crucially — published machine-checkable Lean 4 certificates for each. That last detail is what separates this from the usual benchmark theater. As reported by @Nefarious_Trey, the results include a construction relevant to the non-sofic group question and progress on several Erdős problems, with the solution search costing roughly $2,000 per problem.
The significance is not that a model produced answers. It's that the answers arrive with a formal proof object that a proof assistant can verify independently, without trusting the model's reasoning at all. Lean 4 does not care whether the argument came from a graduate student, a supercomputer, or a language model. If the certificate checks, the theorem holds. This is the cleanest possible signal in a field otherwise drowning in unfalsifiable capability claims.
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