北京协和医院神经外科博士后金山木利用OpenAI的GPT-5.6-Sol模型，用约16小时成功证明了Crouzeix猜想[1]。这一困扰数学界长达22年的问题由法国数学家Michel Crouzeix于2004年提出[1]。美国康奈尔大学数学家Alex Townsend、华盛顿大学教授Anne Greenbaum以及猜想提出者Michel Crouzeix本人均已审阅论文并确认证明正确[1]。
金山木采取非传统路径完成了这项工作，通过设定特定提示词让AI模型在物理断网环境下独立完成证明，全程未进行干预[1]。其学术背景为北京大学地质学专业、协和医学院神经外科博士后，仅接受过理工科本科基础数学教育[1]。他已在GitHub开源全部研究资料[1]。
根据研究历史，2007年Crouzeix本人仅证明了常数在11.08时成立；2017年全球专家将常数进一步降至2.414[1]。2026年8月初，数学家Emiel Lorist和Felix Schwenninger也发布了独立5页证明，同样使用ChatGPT 5.6[1]。
Jin Shanmu, a postdoctoral fellow in neurosurgery at Beijing Union Medical College Hospital, has successfully proved the Crouzeix conjecture—a mathematical problem that has remained unsolved for 22 years—using OpenAI's GPT-5.6-Sol model in approximately 16 hours [1]. The proof has been verified by prominent mathematicians including Alex Townsend from Cornell University, Anne Greenbaum from the University of Washington, and Michel Crouzeix, the French mathematician who originally proposed the conjecture in 2004 [1].
Jin's approach departed from conventional methodology; he set specific prompts to enable the AI model to independently complete the proof in an isolated environment without internet access, maintaining a hands-off approach throughout the process [1]. Despite his academic background in geology from Peking University and neurosurgery at Peking Union Medical College, Jin had only received foundational mathematics education at the undergraduate level in science and engineering [1]. The research materials have been made open-source on GitHub [1].
The difficulty of the Crouzeix conjecture had gradually diminished over time: when Crouzeix himself proved it in 2007, the associated constant stood at 11.08, and by 2017, mathematicians worldwide had reduced it to 2.414 [1]. In early August 2026, mathematicians Emiel Lorist and Felix Schwenninger published an independent five-page proof using ChatGPT 5.6, achieving the same result [1].
