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Beijing neurosurgeon uses GPT-5.6 to prove Crouzeix’s conjecture

He said the result came after a 16-hour autonomous run on GPT-5.6-Sol using the ChatGPT Work platform.

Reported · Written up by our desk · China

A Beijing-based neurosurgeon, Jin Shanmu, used OpenAI’s GPT-5.6-Sol on the ChatGPT Work platform to prove Crouzeix’s conjecture, according to SCMP Economy.

Jin said he was originally trying to solve a problem related to brain ultrasounds and, along the way, moved into numerical linear algebra, where the conjecture is posed for matrices and functions.

SCMP Economy described the conjecture as stating 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, a claim attributed to French mathematician Michel Crouzeix.

Jin’s approach, as outlined by SCMP Economy, involved a 16-hour autonomous run on GPT-5.6-Sol, with the work linked to research he began while studying transcranial ultrasounds.

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