OpenAI announced on August 1, 2026 that an internal version of Astra, its next major model family, produced new results on ten open problems in mathematics and theoretical computer science —
OpenAI announced on August 1, 2026 that an internal version of Astra, its next major model family, produced new results on ten open problems in mathematics and theoretical computer science — each unsolved for at least a decade, some for far longer. The total compute cost to find all ten solutions: roughly $2,000 at GPT-5.6 Sol API rates.
The headline result is the first explicit construction proving the existence of non-sofic groups, resolving a question in group theory open since mathematician Mikhail Gromov introduced the concept of soficity in 1999. Astra also produced a disproof of Connes’s rigidity conjecture on von Neumann algebras, new bounds on high-dimensional sphere packing density, and resolved several problems from Paul Erdős’s famous catalogue. OpenAI published a 249-page manuscript alongside machine-checkable Lean 4 proof certificates on GitHub, with a “sorry” count of zero — meaning every step across all ten formalized proofs is fully verified, according to Forbes’ coverage of the release.
Every prior AI capability claim of the past few years has shared the same structural weakness: the company making the claim was also the only party positioned to evaluate it. Astra’s results sidestep that problem by construction. Lean is a proof assistant that verifies mathematical arguments step by step, and because the certificate files are published under an open license, anyone can download them and run the checker independently — turning a marketing claim into something the mathematical community can actually falsify or confirm rather than simply take on trust.
Fields Medalist Timothy Gowers said he would recommend one of the results for publication in Annals of Mathematics without hesitation. Thomas Bloom, who maintains the Erdős problem catalogue, called the results “big news,” more significant than an earlier unit-distance counterexample OpenAI’s models produced in May. OpenAI’s own Noam Brown added a note of restraint: “Sadly, no Millennium Prize Problems (yet).” Independent observers have also flagged that critics are questioning problem selection and the fact that Astra itself remains unreleased and inaccessible for outside testing — the verification applies to the proofs, not to the general capability of the model that produced them.
OpenAI has not decided whether Astra will ship as GPT-5.7, GPT-6, or under another name entirely, and has given no public release date. What is confirmed: CEO Sam Altman demonstrated Astra to policymakers in Washington, D.C. this week, and the model is expected to be the first system evaluated under the Trump administration’s AI pre-review framework — the same voluntary frontier-model review process that missed its own August 1 formalization deadline. That timing means Astra’s public debut, whenever it happens, will likely be the first real-world test of a review process that, as of this week, still doesn’t formally exist.
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