A neurosurgery resident proved the 22-year-old Crouzeix conjecture with GPT-5.6 Sol

A neurosurgery resident with no formal advanced math background proved a conjecture that stumped mathematicians for 22 years. His collaborator was GPT-5.6 Sol.

From the operating room to matrix analysis

Shanmu Jin is a resident physician in the neurosurgery department of Peking Union Medical College Hospital. His clinical research focuses on transcranial ultrasound, getting sound waves through the skull’s complicated geometry, and that work kept dragging him into matrix analysis. That is how he ran into the Crouzeix conjecture, open since 2004: applying a function to a matrix can grow its norm by at most a factor of two over the function’s maximum on the matrix’s numerical range.

Per Chinese tech outlet 36Kr, Jin ran GPT-5.6 Sol autonomously for 16 hours on the ChatGPT Work platform to close the proof. SIAM News, the numerical analysis community’s own publication, ran an essay under the title “The Neurosurgery Resident Who Proved Crouzeix’s Conjecture.”

Why this one lands differently

AI labs have been publishing mathematical results for months. This case is different in kind: it was not a lab demo. It was a working doctor with a clinical problem, consumer access to a frontier model, and a habit of poking at mathematics on the side.

Days earlier, Anthropic reported that a research version of Claude pushed the lower bound on the fraction of Riemann hypothesis zeros satisfying the hypothesis from 41.6% to 67.2%. Two results in one week, one from a lab and one from a hospital, suggest AI-assisted mathematics is no longer a demonstration category. The tools have reached the people who simply have problems to solve.