Four days after I published a piece arguing LLMs can't make the jump, OpenAI announced that an internal model called Astra had solved ten open problems in mathematics and theoretical computer science. One of them had been open since 1999. I'm not going to pretend that's a comfortable coincidence to sit with. So let's sit with it properly instead of pretending it didn't happen. The headline result is a non-sofic group. Mikhail Gromov introduced the concept of soficity in 1999 and asked...