OpenAI's Astra solves ten major mathematics problems

OpenAI has disclosed that an internal version of Astra, described as its next major model, has solved ten previously open problems in mathematics. The model operates with remarkable efficiency: the total computational cost—measured in tokens consumed during inference—amounts to roughly $2,000 at current Sol API pricing.

The workflow for each solution follows a structured pipeline. First, Astra generates the mathematical argument. Second, human researchers prepare these raw outputs into formal manuscripts suitable for publication or presentation. Third, Astra formalizes each argument in Lean, a proof assistant that verifies correctness at the symbolic level. This formalization step is crucial: it ensures that the solutions are not merely plausible-sounding prose but mathematically airtight proofs. Lean certification is a gold standard in formal verification, so solutions that pass this step represent genuine mathematical advances, not speculative outputs.

OpenAI is also releasing narrations of the model's reasoning process for each of the ten solutions. This transparency move allows researchers and practitioners to inspect how Astra approaches mathematical problem-solving step by step.

The significance of this result lies in reversing a long-standing limitation. Large language models have historically performed poorly on mathematics, a gap that researchers and observers frequently cited as evidence of fundamental gaps in reasoning. Astra's ability to solve open problems suggests that capability gap is narrowing, at least at the frontier. However, the article does not specify whether Astra represents a dramatic leap beyond prior OpenAI models like Fable and Sol, only that "we do know that Astra can do math. As in real math."