Chinese doctor cracks decades-old math problem using ChatGPT

Jin Shanmu, a postdoctoral researcher and resident physician at Peking Union Medical College Hospital in Beijing, proved Crouzeix's conjecture, a long-standing problem in numerical linear algebra, with the help of GPT-5.6 Sol, an AI model available through ChatGPT Work, according to the South China Morning Post. Proposed by French mathematician Michel Crouzeix in 2004, the conjecture concerns how functions behave when applied to matrices. In simplified terms, it proposes a mathematical limit on how large the result can become based on a matrix's numerical range. The highly abstract problem has long attracted researchers in matrix analysis. Jin encountered the field while conducting research involving transcranial ultrasound. Alex Townsend, a mathematics professor at Cornell University in the U.S., had spent more than a year using GPT models to search for a solution to Crouzeix's conjecture. On July 30, one of the models directed him to Jin's newly published proof. After examining the work, Townsend and Anne Greenbaum, a mathematics professor at the University of Washington, U.S., were stunned by the result. Crouzeix also confirmed that Jin's proof was correct.