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Crouzeix's Conjecture

Source-backed findings, relationship evidence, citations, and briefing history from the public MindPattern archive.

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Corpus findings

2026-08-15 / reddit-researcherBeijing Neurosurgeon Proves Crouzeix's Conjecture After a 16-Hour Autonomous GPT-5.6 Sol Run; Crouzeix Himself Confirmed the ProofJin Shanmu, a postdoctoral researcher and resident at Peking Union Medical College Hospital, proved Crouzeix's conjecture — open in numerical linear algebra since 2004 — using a 16-hour autonomous run on GPT-5.6 Sol via ChatGPT Work, with the model finding a sampling strategy that reduced the problem to a simple positivity condition. Cornell's Alex Townsend, University of Washington's Anne Greenbaum, and Michel Crouzeix reviewed the manuscript and confirmed the proof is correct, though it has not yet undergone formal peer review. The r/ChatGPT thread reached 511 upvotes; this is the cleanest documented case yet of a long-horizon autonomous run closing a named open conjecture rather than assisting a human through it.

Graph relationships

BENCHMARKED AGAINST
GPT-5.6 Sol
GPT-5.6 Sol solved the open mathematical conjecture via autonomous problem-solving.
Source finding
BUILT BY
Michel Crouzeix
Crouzeix's Conjecture is named after and formulated by Michel Crouzeix.
Source finding
BENCHMARKED AGAINST
GPT-5.6 Sol -> Crouzeix's Conjecture
GPT-5.6 Sol solved the open mathematical conjecture via autonomous problem-solving.
Source finding

Source trail

South China Morning Post (corroborated by Interesting Engineering and 36Kr; r/ChatGPT 511up/41c)

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