Chinese doctor stuns maths world by cracking decades-old problem using ChatGPT
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. Instead, the self-taught maths enthusiast, with help from OpenAI’s latest flagship artificial intelligence (AI) model, solved a two-decade-old mathematical puzzle that had frustrated experts around the…
A Chinese neurosurgeon named Jin Shanmu stunned the maths world by solving a decades-old problem using OpenAI's ChatGPT AI model. The problem, known as Crouzeix's conjecture, had baffled experts since 2004. Jin, a postdoctoral researcher at Peking Union Medical College Hospital, used a 16-hour autonomous run on GPT-5.6-Sol to crack the puzzle.
The conjecture, proposed by French mathematician Michel Crouzeix, states 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. Mathematicians Alex Townsend and Anne Greenbaum from Cornell University and the University of Washington revealed that Jin had solved the problem after receiving an email from ChatGPT suggesting a solution they had just published.
Both Townsend and Greenbaum, as well as Crouzeix himself, confirmed the accuracy of Jin's proof, although it has not yet undergone formal peer review. Jin's achievement is all the more remarkable given his lack of formal mathematical training, as he is an undergraduate geology major who later transitioned to medicine. This breakthrough underscores how quickly frontier AI systems are advancing and their growing role in driving mathematical discoveries.
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