Neurosurgeon Proves 22-Year-Old Crouzeix Conjecture Using ChatGPT
Jin Shanmu, a neurosurgery resident at Peking Union Medical College Hospital with no advanced mathematics background, has proved the Crouzeix conjecture—a major open problem in numerical linear algebra—using ChatGPT. The result has been acknowledged by Crouzeix himself, and the decisive proof emerged from a roughly 16-hour autonomous GPT-5.6 Sol run. The crossover breakthrough highlights the potential of general-purpose LLMs to help non-specialists tackle frontier theoretical research, drawing wide attention from academia and the tech community.
Confirmed
- The Crouzeix conjecture, proposed in 2004, concerns the optimal constant 2 for operator norms of complex matrices and had remained open for 22 years.
- Jin is a neurosurgery resident (reported alternatively as a doctoral student) at Peking Union Medical College Hospital with an undergraduate degree in geology from Peking University and no professional math training; he entered the problem through transcranial ultrasound research and taught himself matrix analysis.
- According to media reports, he used an adapted "god-tier prompt" and disabled ChatGPT's external search; the decisive proof came from a 16-hour autonomous GPT-5.6 Sol run.
- Mathematician Steven Strogatz shared the case; Microsoft researcher Sébastien Bubeck said he was stunned, recalling that he spent a full week in 2012 trying to crack the problem without success.
Unconfirmed
- Details of the prompt used remain undisclosed despite community discussion.
Why it matters
- The case breaks the assumption that frontier math problems require professional mathematicians, showing that LLMs like ChatGPT can serve as effective research tools enabling cross-domain talent to solve long-standing open problems; several commenters expect more such AI-assisted research cases to follow.
2026-08-12 ~ 2026-08-14 · 11 related posts
Primary sources
- [source] Neurosurgery Resident Solves Major Math Problem Using ChatGPT — stevenstrogatz · 2026-08-12
- Neurosurgery Resident Proves 22-Year-Old Math Conjecture Using ChatGPT — stevenstrogatz · 2026-08-13
- [source] Peking Union Doctor Proves 22-Year Math Conjecture Using ChatGPT — 新智元 · 2026-08-13
- [source] AI Solves 20-Year-Old Crouzeix Conjecture via 16-Hour Autonomous GPT Run — Dr_Singularity · 2026-08-13
- Neurosurgery Resident Solves Major Open Math Problem Using ChatGPT — burny_tech · 2026-08-14
- Neurosurgery Resident Uses GPT-5.6 Sol to Prove 20-Year-Old Math Conjecture — New_Equinox · 2026-08-14
- Neurosurgery Resident Uses ChatGPT to Solve Major Math Problem — dotey · 2026-08-14
4 near-duplicate retellings: stevenstrogatz · stevenstrogatz · asusarla · DeryaTR_