Open since 2004, this numerical linear algebra conjecture gave way to a neurosurgery resident with no training in advanced mathematics, guiding a model in autonomous operation.
Jin Shanmu is a neurosurgery resident and postdoctoral researcher at Peking Union Medical College Hospital. His bachelor's degree is in geology, his doctorate in medicine: no advanced training in mathematics. However, he has produced a proof of the Crouzeix conjecture, a numerical linear algebra statement that has remained open since 2004.
The decisive argument emerged during a sixteen-hour autonomous execution of GPT-5.6-Sol on the ChatGPT Work platform, driven by a command that Jin himself had worked on for a long time. The human role therefore shifted: no longer to produce reasoning, but to frame the problem with enough precision so that a long automatic exploration had a chance of succeeding.
The episode, reported on August 14, 2026, fuels a still open debate about what it means to "solve" a mathematical problem in the age of reasoning models. It also illustrates a broader shift: access to assisted demonstration tools is no longer reserved for mathematics departments.
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