OpenAI has an unreleased model called Astra, and in early August the company said it had used it to crack ten open problems in maths and theoretical computer science. Some of those problems had sat unanswered for a decade. One had been open since 1999.
The headline result is an explicit construction of a non-sofic group, closing a question the mathematician Mikhail Gromov raised nearly 30 years ago. The rest of the list spans group theory, von Neumann algebras, high dimensional geometry, quantum complexity, lattice cryptography and extremal combinatorics, which is a way of saying Astra was not just good at one narrow trick. It was good across fields that barely talk to each other.
Models claiming to "do maths" is not new, and it usually means solving competition style problems that already have known answers buried somewhere in the training data. This is not that. These were genuinely open problems, meaning nobody had a verified answer before Astra produced one.
The part that should make you sit up is the proof format. Every one of the ten solutions shipped with a Lean 4 certificate, which means the proof was checked by a formal verification system rather than just read by a human and nodded through. Lean does not care how confident the output sounds. It either compiles or it does not. That removes the usual complaint about AI generated maths, which is that a fluent wrong answer looks exactly like a fluent right one until someone checks it by hand.
OpenAI put the total compute cost for all ten proofs at roughly 2,000 dollars. For comparison, a single human mathematician working on one of these problems might spend years on it, assuming they crack it at all. That price tag is going to get quoted a lot, and it should, because it reframes what "expensive research" even means once a model can attempt this many open questions in one run.
Astra itself is not public. OpenAI has not said when, or if, it will ship as a product people can use. What it has done is put a marker down: research grade mathematical reasoning, checked and verifiable, is now a thing a frontier lab can demonstrate rather than promise.
This lands in the middle of a long running argument about whether large models actually understand anything or just remix what they have seen. A machine checked proof of a previously open problem is hard to wave away with that objection. It does not prove general understanding, but it does prove the specific claim: this model produced a correct, novel piece of mathematics, and a formal verifier agrees.
It also raises the bar for what "useful AI research assistant" means going forward. Pattern matching against existing papers was already table stakes. Producing checkable, original results in fields as different as cryptography and geometry, in the same run, is a different order of claim, and one that other labs will now be measured against.
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