Chinese doctor stuns maths world by cracking decades-old problem using ChatGPT

Chinese doctor stuns maths world by cracking decades-old problem using ChatGPT Jin Shanmu, a Beijing-based neurosurgeon, was trying to solve a problem related to brain ultrasounds. Instead, he made mathematical history When Beijing-based neurosurgeon Jin Shanmu pulled up a chair at his computer, he was not looking to make mathematical history. He was simply trying to crack a problem related to brain ultrasounds. Jin, a postdoctoral researcher and resident at the Peking Union Medical College Hospital, managed to prove Crouzeix’s conjecture, a problem in numerical linear algebra. His tool? A 16-hour autonomous run on GPT-5.6-Sol, operating on the ChatGPT Work platform. Proposed by French mathematician Michel Crouzeix, the conjecture posits 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. While abstract, it has long been an intriguing problem in matrix analysis – a field Jin stumbled into while undertaking research on transcranial ultrasounds. [Image text:] sin=+care SCe ote ar ont Tan=+ 40 Im $Ed V-m Bde-Id source E4=E+dEh-Eh hadE =BA=Bhdx s+d d-hdxdB Ed=-do spxpry--3py 5d=MI+ h.ds-hdx E-MEE H VE HO No-oadpf VT. I=Icse I-Isine P H 2N390 OH-O -6-DINEXANOACID CH (AnB=AUB' (AUS)-AnS n(AUS) 8V)u-sy+V= nAUBUCnA+n+nc) CH0+60++0 AT exp(xa)d C(xt)= 2t 2DE exp-udu JH. 360 sincrf=1and erf-2=-erf CH,- [1erf] 50Cxt)= WH 1-6DAMINOHEXAN HO, cH-n CH-CH OH CHCH HO ETHYLENE 2AIBG+3C-2AIC+3B TEREPHTHALC ACID CLYCOL OH +HOn +nHO -H H