Shanmu Jin, a neurosurgery resident at Peking Union Medical College Hospital with an undergraduate geology degree, proved Crouzeix's Conjecture on July 27, 2026 using a 16-hour autonomous run of GPT-5.6 Sol in ChatGPT Work mode. The proof addresses a matrix-analysis problem posed in 2004 that had resisted academic attack for 22 years.
The breakthrough
Jin encountered the problem while researching transcranial ultrasound and taught himself the necessary mathematics. He configured the model with no internet access and used swarms of subagents testing strategies against each other. Michel Crouzeix, who posed the conjecture, along with Cornell's Alex Townsend and Anne Greenbaum, verified the manuscript is correct, though formal peer review is pending.
Eight days later, two other mathematicians, Emiel Lorist and Felix Schwenninger, posted an independent proof and disclosed they also used ChatGPT 5.6. Both proofs emerged from prompting strategies rather than traditional academic research pipelines.
Why it matters
Mathematics is entering an era where expertise matters less than access and prompt design. Jin's success demonstrates that frontier AI can solve hard problems autonomously, but it also highlights a sovereignty gap: the proof is reproducible and verifiable by anyone, but the model that generated it is available only through OpenAI's paid API. When the next unsolved problem falls to an AI agent, the question isn't just who gets credit—it's who controls the toolchain.