Peking Union Doctor Proves 22-Year Math Conjecture Using ChatGPT
新智元 · wechat · 2026-08-13
Shanmu Jin, a neurosurgery resident at Peking Union Medical College, successfully proved the 22-year-old "Crouzeix's Conjecture" in applied mathematics using ChatGPT.
- Cross-discipline Breakthrough: Without a formal advanced math background, Jin encountered the conjecture while studying matrix analysis for medical ultrasound research. He used a modified mega-prompt that cut off web access, forcing the model to use multi-branch exploration and adversarial auditing.
- Autonomous AI Run: After setting the instructions, GPT ran autonomously for about 16 hours, undergoing tens of thousands of iterations. It finally cracked the proof using a clever sampling strategy that reduced the problem to a simple positivity condition.
- Academic Shockwave: The conjecture's creator, Michel Crouzeix, and other experts verified the proof. Just 8 days later, two other mathematicians—also using ChatGPT—published a 5-page independent proof.
Jin has open-sourced the paper, prompts, and Lean4 formalization code. This marks a milestone in AI accelerating scientific discovery and breaking down academic barriers.
Related event: Neurosurgeon Proves 22-Year-Old Crouzeix Conjecture Using ChatGPT(11 posts)→
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