Doctor Solves 20-Year Math Problem Using ChatGPT

When Jin Shanmu sat down at his computer last July, he was trying to solve a problem about brain ultrasounds for his neurosurgery research. Instead, he accidentally made mathematical history.

Jin, a doctor at Peking Union Medical College Hospital, proved Crouzeix's conjecture using OpenAI's GPT-5.6-Sol model. The mathematical puzzle had stumped experts worldwide since French mathematician Michel Crouzeix proposed it in 2004.

The breakthrough gets even more remarkable when you learn Jin's background. He studied geology as an undergraduate before switching to medicine. His formal math education never went beyond basic undergraduate science requirements.

Everything else? Self-taught.

Jin fed the problem to ChatGPT and let it run autonomously for 16 hours on the Work platform. On July 27, he uploaded his proof online. Three days later, Cornell mathematician Alex Townsend discovered it after routinely asking GPT models about unsolved problems.

Townsend, University of Washington professor Anne Greenbaum, and Crouzeix himself reviewed Jin's manuscript. All three confirmed the proof was correct, though formal peer review is still pending.

The Ripple Effect

Jin's achievement signals a turning point in how humans and AI can collaborate on complex problems. You don't need decades of specialized training anymore when you can partner with advanced AI systems.

OpenAI reported in May that one of its models autonomously solved an 80-year-old geometry problem from 1946. This month, the company announced its upcoming Astra model had made major progress on 10 more mathematical puzzles. Rival firm Anthropic said its unreleased Claude model recently made unexpected advances on problems related to the famous Riemann hypothesis.

The combination of human curiosity and AI capability is unlocking solutions that seemed impossibly out of reach just months ago. Jin was researching transcranial ultrasounds when he stumbled into the world of matrix analysis. His practical medical problem led him straight to pure mathematics.

What makes this moment special isn't just that a hard problem got solved. It's that someone outside traditional academic mathematics, armed with determination and the right tools, could make a contribution experts thought would take years more work.

The future of discovery might look a lot like Jin: curious people from any background, asking big questions, and finding answers we never expected.