OpenAI's Astra solves 10 open math problems for $2,000

On August 1, 2026, OpenAI announced that an internal version of Astra, its next major model family, solved ten previously open problems in mathematics and theoretical computer science. The company published formal Lean proofs on GitHub, a verification system that lets computers check each step of a mathematical argument. The entire effort cost approximately $2,000 in compute—a fraction of the millions typically spent on frontier AI training runs. Notably, this is not just a typical benchmark improvement: these are unsolved problems that had stumped human researchers. The Lean proofs provide verifiable evidence that Astra's reasoning is sound, rather than relying on hallucinated or unverified answers.

This debut positions Astra as a genuine research tool, not merely a more capable chatbot. The model appears to combine generated hypotheses with formal verification, allowing it to explore solution spaces in math and theoretical computer science. For professional researchers, this could accelerate discovery in areas like topology, combinatorics, and complexity theory. OpenAI has not yet announced when the full Astra family will be publicly released, but the GitHub repository with the proofs is available for scrutiny. The $2,000 compute figure suggests that advanced reasoning no longer requires massive infrastructure; it could make AI-driven mathematics accessible to smaller labs and universities. Whether Astra can generalize to other fields like physics or chemistry remains to be seen, but this proof-of-work is a signal that AI can contribute original, verifiable research results.