OpenAI's Astra model solved 10 decades-old math problems for about $2,000

On August 1, 2026, OpenAI said an internal version of Astra, described as its next major model family, produced machine-checkable solutions to ten open problems in mathematics and theoretical computer science. The questions span group theory, high-dimensional geometry, quantum complexity, and several other fields, and some had been unresolved for decades. OpenAI put the total compute cost for all ten at roughly $2,000 at its own API rates.

The receipts are public

Every proof was formalized as a Lean 4 certificate and published on GitHub, so a mathematician doesn't have to trust OpenAI's framing to check the work. The certificates either verify or they don't. OpenAI also released reasoning walkthroughs for each solution. Its report says "the mathematical arguments themselves, however, came from Astra," notes that humans helped turn the arguments into publishable papers, and points to the Leiden Declaration on AI and Mathematics for how it assigns credit.

The price tag is the headline

Ten novel, independently checkable results for $2,000 in compute is a value-per-dollar number. It is the number this site asks of any AI spend claim: what it cost, what came out, and how a stranger can verify it. A dollar figure paired with a machine-checkable output is closer to an audit trail than most AI research announcements get. Hold other vendor claims to the same standard.