TL;DROpenAI says its unreleased Astra model solved ten open maths problems, shipping Lean proofs on GitHub for roughly $2,000 in compute
OpenAI says an internal version of its next major model, called Astra, has produced ten new results in mathematics and theoretical computer science. Each of the problems had been open for at least a decade. The company published a 249-page manuscript alongside machine-checkable Lean 4 certificates for every result on GitHub.
The headline result is the first-ever explicit construction of a non-sofic group, resolving a central question in group theory that has stood since Mikhail Gromov introduced the concept of soficity in 1999. No mathematician had managed to prove or disprove whether non-sofic groups exist in the 27 years since.
The other results span several fields. Astra disproved Connes’s rigidity conjecture on von Neumann algebras, proved Ehrhart’s volume conjecture, and resolved three problems from Paul Erdos’s famous catalogue, including problem number 183 on multicoloured Ramsey numbers. It also produced the first improvement to the general upper bound on high-dimensional sphere-packing density since 1978, proved a parallel repetition theorem for two-player quantum games, and established new lower bounds on the circuit complexity of computing the permanent.
