OpenAI has a new way of introducing a model: skip the livestream, publish math.
On August 1, the company revealed that an internal version of Astra — the system it calls its next major model — has solved ten open problems in mathematics and theoretical computer science. Not benchmark puzzles. Actual open questions, each unsolved for at least a decade, now sitting on GitHub with proofs anyone can check.
The one mathematicians can't stop talking about
The headline result answers a question that's been open since 1999, when Mikhail Gromov introduced the concept of "sofic" groups. For 27 years, nobody could say whether a non-sofic group existed. Astra constructed one.
That's the kind of result careers get built on, and it didn't come alone. The batch also includes a claimed counterexample to Connes's rigidity conjecture on group von Neumann algebras, improved upper bounds for sphere packing in high dimensions, exponentially stronger bounds for binary and spherical codes, an n⁴/log n lower bound for computing the permanent, and a superexponential lower bound for multicolor Ramsey numbers — which settles Erdős problem 183, one of the puzzles the famously prolific mathematician left behind.
Proofs you don't have to trust
Here's what separates this from earlier "AI does math" headlines: every result ships with a machine-checkable certificate written in Lean, a formal proof language. A Lean proof either compiles or it doesn't. There's no room for the confident-but-wrong reasoning that has burned AI math claims before.
OpenAI published all ten certificates alongside walkthroughs of the model's reasoning. Mathematicians who saw preprints have reviewed the work informally, and the early reactions are striking. Fields Medal winner Timothy Gowers said he'd recommend one of the proofs for a top journal "without hesitation."
The caveat: none of the results has been through formal peer review yet. The Lean certificates verify the logic, but the mathematical community will still want to digest what the constructions actually mean.
The $2,000 detail
Buried in the announcement is maybe its most disruptive number. Total compute for all ten solutions came to roughly $2,000 at OpenAI's Sol API rates.
Ten open problems. Twenty-seven years of stuck questions, in one case. Two grand.
If that figure holds up, it changes the economics of mathematical research in a way that's hard to overstate. Research mathematics has always been constrained by the number of brilliant people willing to spend years on problems that might never crack. Astra's pitch is that some of those problems now cost less than a used laptop to attempt.
What OpenAI is actually announcing
Astra itself isn't available. There's no release date, no product page — just the proofs. That's the point. Rather than promising capabilities, OpenAI dropped artifacts that demonstrate them, and let mathematicians kick the tires.
It's also a signal of where the frontier labs think the next competitive battle is: not chat, but verified scientific reasoning. A model that can produce formally checkable proofs isn't just autocomplete with better marketing. It's a research instrument.
What happens next
Watch for three things. First, whether the proofs survive close reading — Lean verifies the steps, but mathematicians will scrutinize the definitions and constructions behind them. Second, whether the non-sofic group construction opens new territory, since answers to old questions tend to generate new ones. Third, what the shipping version of Astra looks like, and whether the research-grade reasoning survives contact with a consumer product.
However it plays out, August 1 will be a date math historians remember. The proofs are public, the certificates compile, and the question is no longer whether an AI can settle open mathematics. It's how many more problems are about to fall.
