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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

9 votes

Not especially famous, long-open problems which anyone can understand

The following conjecture by Carsten Thomassen: If $G$ is a 3-connected graph, every longest cycle in $G$ has a chord. Thomassen has proven the conjecture true for 3-connected cubic graphs.
6 votes

Favorite popular math book

Title: The Mathematician's Brain Author: David Ruelle Short description: (++) A book describing how Mathematics are founded, and tries to give a reasoning for the brain-work needed to do math. Fro …