OpenAI's next model solves 10 math problems
An internal build of OpenAI's unreleased Astra model produced ten new results in math and theoretical CS, each backed by a machine-checked Lean proof on GitHub.
OpenAI published ten new results on August 1 in fields including high-dimensional geometry, coding theory, group theory, arithmetic circuit complexity, and extremal combinatorics, problems the company says had seen no progress on their main result for at least a decade, in several cases much longer. Two results resolve named open problems: Erdős problems 146, 180, and 183 among them, according to OpenAI’s own accounting. The company credits the work to an internal version of Astra, described only as “our next major model,” which has not otherwise been announced or released.
What separates this from a typical model-capability claim is the proof format. Alongside the blog post, OpenAI published a technical paper, a set of reasoning walkthroughs, and, for every one of the ten results, a formal certificate written in the Lean 4 proof assistant and posted to a public GitHub repository. Lean proofs are machine-checkable: anyone can run lake build against the repository and have the proof assistant itself confirm the logic holds, without trusting OpenAI’s word or Astra’s reasoning trace. The ten formalizations include an improved sphere-packing bound reaching the Cohn-Elkies threshold, exponentially stronger bounds for binary and spherical codes, a construction of a non-sofic group, a counterexample to Connes’s rigidity conjecture, and a new $n^4/\log n$ lower bound for arithmetic circuits computing the permanent.
What it means for operators
Model providers claim benchmark wins constantly, and most of those claims are impossible for an outside party to independently check without redoing the work. Publishing a Lean certificate alongside each claim removes that trust gap entirely for formal domains: the proof either compiles against a general-purpose proof assistant or it doesn’t. If your organization evaluates frontier models on reasoning-heavy tasks, this is worth watching as a template, not just a math result, because the same self-verification pattern (a claim plus an artifact a third party can mechanically check) is the direction serious capability evidence is heading, well beyond math. Astra itself remains unreleased, so there is no product decision to make here yet, only a capability signal to track against whatever OpenAI ships next under that name.