OpenAI Astra Solves Ten Decade - Old Math Problems With Machine - Checkable Lean Proofs

OpenAI's unreleased Astra model has produced what its October 2025 announcement only pretended to: genuine solutions to ten long-standing open problems in mathematics and theoretical computer science, each accompanied by a machine-checkable Lean 4 certificate that any reader with a laptop can verify independently. The proofs — spanning group theory, von Neumann algebras, high-dimensional geometry, quantum complexity, lattice cryptography, and extremal combinatorics — were published August 1 alongside a 249-page technical manuscript and a 62-page account of how the arguments came together. Every Lean 4 certificate file is publicly available on OpenAI's GitHub repository under an Apache 2.0 license. That last detail is not a footnote. It is the structural change that separates this announcement from every prior AI-mathematics milestone. When OpenAI's model disproved the Erdős unit distance conjecture in May 2026, the validation came from nine external mathematicians reading and signing off on the argument — a social signal, strong but not reproducible without the same expertise. A Lean certificate is different. Lean 4's trusted kernel gives a binary verdict: the proof either compiles or it doesn't. No PhD required. No months-long peer review backlog. Anyone can run the check. Thomas Bloom, the University of Manchester mathematician who curates…