Beijing Doctor Uses GPT-5.6 to Prove a 22-Year-Old Math Conjecture

Jin Shanmu proved Crouzeix's conjecture, open since 2004, in a 16-hour autonomous run on GPT-5.6 Sol through ChatGPT Work. The model found a sampling strategy that reduced the problem to a simple positivity condition, per South China Morning Post.

Crouzeix's conjecture had resisted proof for more than two decades. This is the cleanest documented case yet of a long autonomous run closing a named open problem instead of assisting one.

Three people who matter checked the work. Cornell's Alex Townsend and University of Washington's Anne Greenbaum reviewed the manuscript. So did Michel Crouzeix, the mathematician the conjecture is named after. All three confirmed the proof is correct. It hasn't gone through formal peer review yet, and the source doesn't say when that review will happen or where the proof will get published.

That gap matters more than the headline. A named mathematician confirming a proof by eye isn't the same as a journal accepting it. Math has a history of proofs that looked solid under informal review, then failed under formal scrutiny. Until a journal runs its process, call this confirmed-by-experts, not settled.

Autonomous, not assisted

The detail that separates this from typical AI-and-math stories is the length of the run. Sixteen hours is long enough that Jin wasn't steering each step. The model picked a strategy, ran with it, and produced a proof that a doctor then took to three specialists for confirmation. Most AI-math coverage this year has covered assistance, a model suggesting a lemma or checking algebra. This is closer to a model doing the mathematical work end to end on a named, dated open problem.

No transcript or reasoning trace from the 16-hour run is public yet. The record so far is a result and three confirmations, not a way to see how the model got there.