Chinese Neurosurgeon Uses ChatGPT to Prove Decades-Old Math Conjecture

Jin Shanmu, a neurosurgeon and postdoctoral researcher at Peking Union Medical College Hospital in Beijing, has made headlines in the mathematics community by successfully proving Crouzeix's conjecture, a long-standing issue in numerical linear algebra. This significant achievement was not reached through conventional mathematical techniques but rather via a 16-hour autonomous session on GPT-5.6-Sol, utilizing the ChatGPT Work platform. Initially focused on brain ultrasounds, Jin unexpectedly ventured into matrix analysis. Crouzeix's conjecture, introduced by the French mathematician Michel Crouzeix, asserts that the norm of any function applied to a matrix does not exceed twice the function's maximum value on the matrix's numerical range. Jin's accomplishment illustrates the increasing influence of AI in scientific exploration, showcasing how large language models can tackle intricate mathematical challenges. The mathematical community has reacted with astonishment, as this proof was generated by a non-mathematician utilizing AI technology, highlighting AI's potential to democratize advanced research and expedite breakthroughs in various fields.