Ten Advances in Mathematics and Theoretical Computer Science
Source: OpenAI, August 1, 2026
Authors: OpenAI (results by an internal version of Astra, their next major model; manuscripts prepared by humans with the same model)
What it is
OpenAI’s announcement of ten results on problems that had been open with no progress on the main result for at least a decade — spanning high-dimensional sphere packing, coding theory, non-sofic groups, Connes’s rigidity conjecture, arithmetic circuit complexity, quantum parallel repetition, lattice cryptography, and extremal combinatorics. The results follow their May AI-generated disproof of the Erdős unit-distance conjecture. Each argument was formalized by the model in a Lean certificate, and OpenAI released the model’s narration of its reasoning for each solution; they note the token cost of finding the solutions was roughly $2,000 at API rates.
Why it’s on the shelf
(Shelf note — Summer’s to write.)
External work — shelved, not authored, by Hearthwell. All claims and credit belong to the original authors.