OpenAI's Astra Cracks Ten Open Math Problems for About Two Thousand Dollars

On August 1, 2026, OpenAI officially confirmed the existence of "Astra," a new model family designed to take on long-horizon research work. Alongside the announcement, the company published a research note showing that Astra has solved ten open problems in mathematics and theoretical computer science, each one untouched for at least a decade and some for far longer. Every proof is paired with a Lean 4 formal verification script, which means the reasoning can be checked by software, not just trusted by eye. In a field where a single missing step can break a whole argument, that kind of machine-checkable certificate is what separates a serious claim from a marketing one.

The ten results cover a wide range of areas: high-dimensional geometry, coding theory, group theory, quantum complexity, and extremal combinatorics. Several of them resolve long-standing open questions left by the Hungarian mathematician Paul Erdos, including a new super-exponential lower bound for multicolor Ramsey numbers. OpenAI also reports that the entire set of proofs cost only about two thousand dollars of compute when billed at the Sol API rate. A single research lab could once spend a whole postdoc salary on that kind of effort; today, the same wall of work runs as one cloud bill.

The story is not only about math. Astra is built as a long-horizon agent system, meaning it can split a large goal across many cooperating agents, run them in parallel, and stitch the results back together into a single coherent argument. Sam Altman demonstrated this capability to United States senators on July 29, including Raphael Warnock and Bernie Moreno, ahead of any public launch. Under the Trump administration's new AI framework, Astra is widely expected to be one of the first frontier models to go through federal review before release, which is why the final name and the release date are still up in the air.

The deeper lesson is that AI has clearly moved past the stage of summarizing human knowledge and is now able to push the frontier of it, at least in narrow, formal domains. The combination of low compute cost, formal verification, and multi-agent coordination makes it possible for small teams to attempt problems that used to require entire research institutes. At the same time, peer review, attribution, and safety review are all still very much open questions. A model that can crack a ten-year conjecture in an afternoon is also a model that needs a much sharper rulebook for how its results reach the world.