OpenAI unveils Astra with ten new math and CS proofs
OpenAI introduced its next major model family, Astra, by publishing ten solutions to long-open problems in mathematics and theoretical computer science.
OpenAI on Friday introduced Astra, which it describes as its next major model family, and chose an unusual launch vehicle: a package of ten research results in pure mathematics and theoretical computer science, each accompanied by a Lean formalization and a chain-of-thought walkthrough.
What was published
The company says an internal version of Astra produced the mathematical arguments, and that human researchers used the same model to write the results up as manuscripts. The problems span high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography and extremal combinatorics. Among them: new upper bounds on sphere-packing density reaching the Cohn–Elkies threshold, exponentially improved bounds on the maximum size of binary codes at a prescribed minimum distance, and a disproof of Connes' Rigidity Conjecture in von Neumann algebra theory.
The headline item is a construction showing that non-sofic groups exist — an infinite, finitely presented group failing Gromov's soficity condition, settling a question he posed in 1999. OpenAI researcher Sébastien Bubeck said on X that each of the ten proofs ships with machine-checkable Lean certificates, published in an accompanying openai/ten-proofs repository. OpenAI says none of the ten problems had seen progress in at least a decade, and most for far longer.
Framing and cost
OpenAI positions Astra as a class of model built for long-horizon work, coordinating multiple agents across hours or days, sitting alongside the existing Sol, Terra and Luna tiers; the eventual product name is not settled. Noam Brown called the results a significant step for scientific reasoning and stressed that the lab did not spend heavily per problem — the ten solutions reportedly cost roughly $2,000 at API rates. Mathematicians who reviewed the output, including Manchester's Thomas Bloom, called the results notable. OpenAI took responsibility for accuracy while attributing the arguments themselves to the model.
Why it matters
Until now, AI contributions to open mathematics have mostly been incremental bound improvements or assistance on human-led proofs. A batch of ten decade-plus-open results — with Lean certificates that remove the usual "can it be verified?" objection, at a cost measured in thousands rather than millions of dollars — is a materially different claim. It also sets the terms for Astra's launch: OpenAI says the model will be the first submitted under the new U.S. framework requiring government review before public release, making its capability case a regulatory argument as much as a scientific one.