OpenAI's unreleased Astra cracked 10 open math problems for $2K

OpenAI dropped ten solutions to open math and theoretical CS problems on August 1 — every one stuck for at least a decade — generated by an internal build of Astra, its unreleased next flagship. The headliners: an explicit non-sofic group construction, open since Gromov posed the question in 1999; a counterexample to Connes's rigidity conjecture; and the first improvement since 1978 to the general high-dimensional sphere-packing exponent.

The interesting part isn't the proofs, it's the receipts. OpenAI published a 249-page manuscript, the model's raw reasoning traces, and Lean 4 proof certificates with a sorry count of zero — meaning no step was left unproven. Total token cost for all ten results: roughly $2,000 at API rates.

The caveats are real. Lean's kernel confirms a proof is logically airtight, not that the formalized statement says what the open problem actually asks. Nothing here has been peer reviewed, and critics are already questioning how the ten problems were selected. Mathematician Thomas Bloom called the results "big news" while noting the system was built by mathematicians and trained on everything mathematicians have ever written.

Why it matters: research claims that ship with machine-checkable certificates instead of benchmark scores change what "trust the model" even means.