OpenAI's Astra model solved 10 decades-old math problems for about $2,000
Every proof is machine-checked in Lean 4 and published on GitHub under an open license -- an unusually verifiable AI research claim, and a rare case where the receipts and the price tag are both public.
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 -- questions spanning group theory, high-dimensional geometry, quantum complexity, and several other fields, some unresolved for decades. OpenAI put the total compute cost for all ten at roughly $2,000 at its own API rates.
The receipts are, unusually, 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 and, per its own report, says "the mathematical arguments themselves, however, came from Astra," while noting humans helped turn the arguments into publishable papers and pointing to the Leiden Declaration on AI and Mathematics for how it's assigning credit.
Why the price tag is the actual headline
Ten genuinely novel, independently checkable results for $2,000 in compute is a value-per-dollar number, not just a capability one -- and it's the same kind of number this site's own methodology is built to demand of any AI spend claim: not "the model did something impressive" but "here is what it cost, here is what came out, and here is how a stranger can verify it." That combination -- a real dollar figure and a machine-checkable output -- is closer to an audit trail than most AI research announcements get, and it's worth noticing precisely because it's rare, not because the size of the number is inherently the point.