OpenAI's Unreleased Astra Model Solves Ten Open Maths Problems

OpenAI has published ten solutions to open problems in mathematics and theoretical computer science, credited to an internal, unreleased version of its next major model, Astra. The results span group theory, high dimensional geometry, coding theory, quantum complexity, lattice cryptography and extremal combinatorics.

The headline result is the first explicit construction of a non-sofic group, a question that has stood open since Mikhail Gromov introduced the idea of soficity in 1999. Astra also produced a disproof of a version of Connes's rigidity conjecture and new bounds on sphere packing. OpenAI says the proofs are machine checkable and has published them as Lean files on GitHub alongside the announcement.

What stands out is the cost. OpenAI estimates the compute needed to reach all ten results would run to roughly 2,000 US dollars at Sol era API rates. That is a strange number to sit next to problems mathematicians have chased for decades, and it is the number most likely to stick with people who do not follow model releases closely.

Astra itself has not shipped. What OpenAI released is a paper and a set of proofs, not a product, so there is no pricing or access to test yet. Independent mathematicians will need time to check the proofs properly before the results can be taken as settled, and OpenAI has invited that scrutiny directly by publishing the Lean files rather than just the headline claims.

For anyone building with AI tools day to day, the practical read is simpler than the maths. A frontier lab is now willing to stake its next flagship release on proof work that used to be treated as a poor fit for language models, output that is either correct or it is not, with no partial credit for a confident wrong answer. If Astra's maths proofs hold up to review, that is a meaningfully different kind of benchmark to the writing and coding demos most releases lead with.

We will be watching for the full Astra release and for independent verification of these results before drawing bigger conclusions. For now it is a striking preview of what a frontier lab thinks is worth publishing ahead of a launch.