Neurosurgeon Jin Shanmu, a researcher at Hospital da União de Pequim, proved the Crouzeix conjecture, a problem in numerical linear algebra that had been open for decades, after a 16-hour autonomous session with the GPT-5.6-Sol model on the ChatGPT Work platform.
Jin is a postdoctoral fellow and resident at the hospital. He was trying to solve a question related to brain ultrasounds when he arrived at the mathematical challenge, which belongs to the field of matrix analysis.
The conjecture
The conjecture was proposed by French mathematician Michel Crouzeix. It states that the norm of the application of any function to a matrix is not greater than twice the maximum value of that function in the numerical range of the matrix.
Although it is an abstract problem, the conjecture is considered relevant in matrix analysis, a field Jin entered during research with transcranial ultrasound.
