OpenAI publishes ten new math results from a model, with machine-checkable proofs

AI math research just crossed a line most people thought was years away. OpenAI has published ten new results in mathematics and theoretical computer science, produced by one of its models.

The collection is called “Ten advances in mathematics and theoretical computer science”, published August 1, 2026. The ten results cover: high-dimensional sphere packing, binary and spherical codes, non-sofic groups, Connes’s rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, the closest vector problem, Ehrhart’s volume conjecture, multicolor Ramsey numbers, and extremal number conjectures.

The headline result

The one to know is the non-sofic group. Mikhail Gromov introduced the notion of soficity in 1999, and the question of whether any group escapes it stayed open for 27 years. Nobody could prove it either way. This collection contains an explicit construction of one, resolving whether every group admits finite permutation approximations.

Receipts, not vibes

Here is what separates this from a model acing a benchmark. OpenAI also published a companion repository, openai/ten-proofs, containing Lean 4 formalizations of all ten results, with build instructions. The logic can be checked mechanically instead of taken on trust. Anyone can clone the repository and run the verification themselves.

Two honest caveats

First, OpenAI’s repository does not name which model produced the results, so treat any specific model name you see in coverage as reporting rather than confirmation. Second, the mathematical community still has to weigh the novelty and the assumptions of each result, and that process will take months.

But the shape of the claim is new: not a model explaining the frontier of human knowledge, a model pushing it, with machine-checkable receipts attached.

Does a machine-checked proof count as real mathematics, or does it need a human author? Mathematicians now have ten concrete cases to argue over.