Chinese neurosurgeon solves long-running matrix problem with ChatGPT

Beijing-based neurosurgeon Jin Shanmu has proved Crouzeix’s conjecture, a long-standing problem in numerical linear algebra, while investigating a challenge related to brain ultrasounds. Jin, a postdoctoral researcher and resident at Peking Union Medical College Hospital, is described as a self-taught maths enthusiast who encountered matrix analysis through research on transcranial ultrasounds.

The breakthrough came with help from OpenAI’s latest flagship AI model. Jin used a 16-hour autonomous run on GPT-5.6-Sol through the ChatGPT Work platform to solve a problem that had frustrated mathematicians around the world since 2004.

Proposed by French mathematician Michel Crouzeix, the conjecture states that the norm of applying any function to a matrix is no larger than twice the function’s maximum value on that matrix’s numerical range. The result links an abstract question in matrix analysis with an unusual path from clinical research to mathematical discovery.