A Beijing-based neurosurgeon has solved Crouzeix's conjecture — a major open problem in numerical linear algebra that had frustrated mathematicians since 2004 — using OpenAI's ChatGPT powered by GPT-5.61,2.
Jin Shanmu, a postdoctoral researcher and resident at the Peking Union Medical College, posed the problem to ChatGPT 5.6 on July 30, 2026, as he had been routinely doing for the preceding year. Jin, described as a self-taught mathematics enthusiast, was not originally pursuing the conjecture for its own sake; he was working on a problem related to brain ultrasounds when the breakthrough emerged.
Crouzeix's conjecture is described as a major open problem in numerical linear algebra that has stood unresolved since 2004. Mathematicians now say the neurosurgery resident's ChatGPT-assisted work constitutes a solution.
The result is notable on two axes: the solver's profile and the tool he used. Jin is not a professional mathematician — he is a practicing neurosurgeon whose engagement with the problem was a side pursuit. The model that produced the key assistance, GPT-5.6, is identified as OpenAI's latest flagship AI model.
ANALYSIS The episode marks a concrete instance of a frontier language model contributing to the resolution of a longstanding, expert-level mathematical conjecture — a category of task that has served as a benchmark for AI reasoning capability. That the user was a domain outsider working on an adjacent applied problem, rather than a specialist attacking the conjecture directly, underscores a shift in how such tools may lower the barrier to contributions in formal mathematics.