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

Beijing-based neurosurgeon Jin Shanmu used OpenAI's GPT-5.6-Sol on the ChatGPT Work platform to prove Crouzeix's conjecture, a two-decade-old mathematical problem in numerical linear algebra, during a 16-hour autonomous run. The proof, achieved while researching brain ultrasounds, resolves a puzzle proposed by French mathematician Michel Crouzeix in 2004 that had frustrated experts worldwide.

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. OpenAI’s latest flagship artificial intelligence AI model https://www.scmp.com/tech/tech-trends/article/3362568/openai-blinks-face-chinese-rivals-drops-pricing-some-models-80?module=inline&pgtype=article , solved a two-decade-old mathematical puzzle that had frustrated experts around the world since 2004. 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.