OpenAI says its next model, Astra, cracked ten maths problems that had been sitting open for a decade or more. The proofs check out. The model does not exist for you.
Here is the thing worth holding onto before the headlines run away with it. Around the 1st and 2nd of August, OpenAI put out a 249-page manuscript claiming Astra generated solutions to ten longstanding problems across mathematics and theoretical computer science, each unsolved for ten years or more. The showpiece is the first explicit construction of a non-sofic group, a question the mathematician Mikhail Gromov opened back in 1999. In plain terms: a group is ‘sofic’ if you can approximate its behaviour with finite shuffling systems, and for 27 years nobody could prove a group existed that broke the rule. Astra, per OpenAI, built one.
Now the bit that makes this more than a press release. Every proof was written in Lean 4, a formal proof language where a machine, not a peer reviewer, checks each logical step. OpenAI published the certificates on GitHub under an Apache 2.0 licence, and the repository’s ‘sorry’ count sits at zero. (‘sorry’ is Lean’s placeholder for a gap you have not filled, so zero means the machine could not find a hole.) That is a real, verifiable claim, and a good deal harder to fake than a benchmark score.
The catch nobody’s putting in the headline
Astra is not a product. There is no release date, no price, no model card, and no way to open a tab and use it. It is a capability announcement dressed in the language of a launch, and a lot of coverage is filing it under ‘OpenAI releases Astra’ when what OpenAI released was a paper about Astra. Those are different things, and the difference is the whole game now.
Two more corrections while we are here, because both are already doing the rounds. First, none of the ten results has been through human peer review yet. Machine-checked is not the same as mathematician-blessed, and formalising a proof can smuggle in assumptions. Second, that widely-quoted ‘$2,000’ compute figure is the total for all ten problems combined, at GPT-5.6 Sol API prices, not the cost per problem. People reading it as $2,000 each are inflating the bill by roughly ten times.
The angle: if a lab can announce a result, capture every headline, and never let you touch the thing, expect a lot more of it. The useful question stopped being ‘is it impressive’ and became ‘when can I actually call it.’ For Astra, the honest answer today is: you can’t.
Did you know: Lean started life as a Microsoft Research project in 2013, and the ‘mathlib’ community library it leans on now runs to well over a million lines of formalised mathematics, most of it written by volunteers.
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