OpenAI dropped a big one on August 1: an internal version of Astra — the model it keeps calling its "next major model" — has solved ten open problems in mathematics and theoretical computer science. Not exercises. Open problems, each stuck for at least a decade. The company backed the claim with a 249-page manuscript and, more importantly, a machine-checkable Lean 4 certificate for every single result, all posted to GitHub.
What it proved
The headliner is the first explicit construction of a non-sofic group. Mathematicians have argued about whether these things even exist since Mikhail Gromov defined soficity back in 1999. Twenty-seven years, no answer. Now there's one.
The rest of the list is just as strange in its breadth. Astra knocked down Connes's rigidity conjecture in von Neumann algebra theory, proved Ehrhart's volume conjecture, and cleared three problems from Paul Erdos's famous catalogue — including number 183, on multicoloured Ramsey numbers. It found the first improvement to the general upper bound on high-dimensional sphere packing since 1978. It proved a parallel repetition theorem for two-player quantum games and pushed the known lower bounds on the circuit complexity of the permanent.
Sebastien Bubeck, who heads OpenAI's mathematics research, confirmed everything on X and called the results "beautiful." Each comes with its Lean certificate and a chain-of-thought walkthrough. And here's the number that stings a little if you're a human mathematician: the compute for all ten cost about $2,000 at Sol API rates.
The certificates are the point
Skeptics of AI-generated math have always had one solid objection — who's going to check a proof that a model spat out? This announcement takes that argument away. A Lean certificate can be verified by anyone with the compiler. You don't have to trust OpenAI, its model, or its marketing. You run the check yourself.
That timing isn't accidental, because the labs and the mathematicians are barely on speaking terms right now. In June, researchers published the Leiden Declaration — endorsed by the International Mathematical Union — accusing AI companies of using published work without consent, dodging peer review, and eroding how proof and credit are supposed to function. One specific complaint: companies announcing theorems in press releases instead of journals. OpenAI announced these ten in a blog post.
Not a one-off
Back in May, the same model family disproved the Erdos unit distance conjecture, a problem that had stood for 80 years. Fields Medalist Timothy Gowers said he'd recommend that proof for the Annals of Mathematics "without hesitation." This time, Thomas Bloom — the mathematician who runs the Erdos problems site — called the ten new results "big news" and rated them above the unit distance work in significance.
Where this goes
Nobody outside OpenAI knows when Astra ships. Investor Mark Kretschmann and others read it as the GPT-6 series; OpenAI won't say. The company is also handing 100,000 academic researchers free frontier-model access through 2027 — generous, and also a way of making itself the infrastructure that research runs on.
The math checks out. That part's settled, and it's the easy part. What's not settled is whether a discipline built on journals and peer review will accept frontier results that arrive by corporate blog post. The Leiden Declaration asked exactly that question in June. Astra just made it impossible to postpone.
Image: Yan Krukau, via Pexels
