ChatGPT Solves Decades-Old Math Problem: Crouzeix's Conjecture

A Chinese doctor has accidentally solved a decades-old math problem using OpenAI's latest AI model. Neurosurgeon Jin Shanmu, based in Beijing, found the proof for Crouzeix's conjecture. This problem had remained unsolved since 2004. Jin, a self-taught mathematician, used the flagship model while working on an issue related to brain ultrasounds. After 16 hours of continuous work, the AI model, GPT-5.6-Sol, found the proof. The conjecture, proposed by Michel Crouzeix, states that applying a function to a matrix never makes it grow larger than twice its expected regional limit. Jin collaborated with professors Anne Greenbaum and Alex Townsend, and Crouzeix himself, to confirm the discovery. Townsend had been trying to solve the conjecture for over a year using other GPT models without success. This breakthrough highlights the potential of AI models to solve complex scientific challenges.