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 whether every countable group has to be sofic. Twenty-seven years, no mathematician managed to prove or disprove it. Astra built the counterexample. The certificate ships on GitHub in Lean 4, formally verified, "sorry" count zero — meaning no step in the proof was left unproven, no trust in OpenAI required. Total inference cost for all ten results combined: about $2,000.
Thomas Bloom, who curates the Erdős problems catalogue at Manchester, called it big news. Worth knowing: Bloom is the same mathematician who publicly dismantled an earlier false OpenAI math claim last October. His endorsement here isn't a company's own press release getting nodded along. It's the field's most skeptical reader saying this one holds.
