OpenAI named its next model family Astra and introduced it with ten solved math problems
An internal version of Astra produced results for ten problems mathematicians had not moved on in at least a decade. The compute bill was about 2,000 dollars, and every proof ships with a machine-checkable certificate.
OpenAI has confirmed the name of its next major model family, Astra, and chose an unusual way to announce it: a report claiming that an internal version of the model produced results for ten open problems in mathematics and theoretical computer science. Mathematicians had made no progress on any of them for at least ten years, and on most of them for far longer.
The list spans several fields. Astra established the existence of non-sofic groups, a long-standing open question in group theory, disproved Connes’s rigidity conjecture on von Neumann algebras, proved Ehrhart’s volume conjecture, and resolved three problems from the Erdos catalogue, the famous list of unsolved puzzles left behind by mathematician Paul Erdos. It also produced the first improvement since 1978 to the general upper bound on how densely spheres can be packed in high dimensions. Two details make this checkable rather than merely impressive. Each proof was formalised in Lean, a programming language built to verify mathematical arguments step by step, so a computer can confirm the logic holds. And OpenAI published a walkthrough of the model’s reasoning for each result. The company says the tokens needed to generate all ten solutions would cost roughly 2,000 dollars at the API rates for its Sol model.
What is behind this. Astra is described as a family designed for long-running work, coordinating several agents on one problem for hours or days rather than answering in seconds. Sam Altman demoed it to policymakers in Washington last week, and it is expected to be the first model to pass through the US government’s planned pre-release review process. Publishing math proofs is a strategically neat way to make the case, because a proof is one of the very few AI outputs that can be verified absolutely rather than argued about. The caveats are real and mostly come from OpenAI’s own people. Researcher Noam Brown noted that the model tried and failed on bigger targets: “Sadly, no Millennium Prize Problems (yet).” Thomas Bloom, the Manchester mathematician who runs erdosproblems.com, called the results big news while rejecting the framing that AI is replacing mathematicians, pointing out that the system was built by mathematicians and trained on everything mathematicians have ever written. Fields Medalist Timothy Gowers has described watching this happen as “very strange and not particularly pleasant”, while still being glad the problems got solved.
What this means for you: nothing today, and Astra has no release date, no confirmed name in the product lineup, and no price. What it tells you is where the frontier is heading: away from “answer my question well” and towards “work on this by yourself for a long time and come back with something”. If you use AI at work, the version of that you will actually meet is a model that takes on a multi-hour task instead of a five-minute one. Worth keeping grounded: mathematics is unusually friendly territory for machines, because an answer can be checked mechanically. Most jobs do not come with a Lean certificate.
Sources
Anthropic checked 141,006 test runs and found three cases where Claude attacked real companies
A misconfigured test environment gave Claude models live internet access during security exercises. Three real organisations were compromised, and one model published malware to a public package registry.
