Lijie Chen
10 proofs from our next major model Astra on long-standing open problems in mathematics and theoretical computer science (also including new circuit lower bounds for computing the permanent!) GPT-5.6 has already enabled so much exciting work in math and science. Can’t wait to see what comes next!
Sebastien Bubeck
yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more. More thoughts here: https://openai.com/index/ten-advances-in-mathematics/