There's one detail that lifts this release off the marketing shelf: each of the ten proofs comes with a Lean certificate - a formal record a machine checks line by line. In May, OpenAI showed a disproof of an Erdős conjecture, found while testing an unreleased model. Today they show ten results at once, and drop the name of their next big model along the way.
Fact
The facts: on August 1, OpenAI published ten results, each of which solves or substantially advances a longstanding open problem - from sphere packing in high dimensions through codes and arithmetic complexity to quantum games and lattice-based cryptography. Three close Erdős problems (146, 180 and 183), one disproves a Connes conjecture on von Neumann algebras, another constructs a non-sofic group - a central open question in group theory. By the company's account, the results were achieved by an internal version of Astra, 'our next big model,' and the tokens for all the solutions would cost about $2000 on Sol API. The manuscripts were prepared by people using the same model, after which it formalized every proof in Lean; descriptions of the reasoning trail were also published. The company takes responsibility for correctness, but states that the mathematical arguments themselves were generated by the system. Source: OpenAI, 01.08.2026.
Why the certificate is what matters. A company's claim about its own model normally gets read with a grain of salt - benchmarks get tuned, wording gets stretched. A formalized proof leaves no room for that argument: it either passes the check or it doesn't. That's why this release carries more weight than any percentage table we've seen this year.
A benchmark gets disputed. A formal proof gets checked.
And the staging is worth noting too. OpenAI could have unveiled Astra on stage, with a demo and applause. Instead the name slips out in passing, inside a math paper. The move is calculated: the message isn't 'look how fast it is,' it's 'it already does a researcher's job.' There's a stronger signal than the staging, too: after the May result, outside mathematicians published their own follow-ups. The community isn't watching from the stands. It's in the game.
The price is what stays with me - about $2000 in tokens against problems generations of mathematicians broke their teeth on. Community verification is still ahead, and some of the shine may fade by then. But the ratio is new. The sharp researcher today asks the model early, before his colleague has asked.
Official primary sources
OpenAI - Ten advances in mathematics and theoretical computer science, 01.08.2026The visual is generated code-art, no third-party images.