Neurosurgeon proves conjecture that stumped mathematicians for 22 years with a 16-hour GPT-5.6 run

Mathematician Alex Townsend had been asking ChatGPT to prove the Crouzeix conjecture for almost a year, but the model consistently gave false or incomplete proofs. On July 30, 2026, ChatGPT returned a link to a preprint posted three days earlier, claiming a solution. Townsend and his colleague Anna Greenbaum read it skeptically and soon realized it was genuine. The author, Dr. Shanmu Jin, is a neurosurgery resident and postdoc, not a professional mathematician. He became interested in the Crouzeix conjecture while working on transcranial ultrasound, and formulated a proof strategy in a 16-hour autonomous session with GPT-5.6 Sol in ChatGPT Work, without internet access. The model used a portfolio of diverse strategies, adversarial audits, and counterexample-based elimination, as prompted by Jin. The proof was independently checked by Townsend, Greenbaum, and Michel Crouzeix, and later strengthened by a second, different proof by mathematicians Emil Lorist and Felix Schwenninger, who also used ChatGPT 5.6 Pro. The case highlights a paradigm shift in mathematical discovery and raises questions about the sustainability of peer review.