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Apr 13, 2022 at 6:21 comment added Kevin Perhaps I have badly misunderstood the premise of the question, but I don't find that proof very explanatory either. Allow me to illustrate: "Q: Why are all maps four-colorable? A: Because all maps can be simplified to one of these four-colorable cases. Q: Why are all of those cases four-colorable? A: Because they are."
Jul 25, 2013 at 8:13 comment added Qiaochu Yuan In general I think arguments that involve a lot of casework tend not to be beautiful but could still be explanatory.
Jul 24, 2013 at 19:18 comment added Noah Snyder This is a good example, but to play Devil's advocate for a moment, the argument basically comes down to discharging and Kempe chains and both of those are kinda beautiful (if old hat by the time of Appel and Haken).
S Jul 24, 2013 at 18:24 history answered Terry Tao CC BY-SA 3.0
S Jul 24, 2013 at 18:24 history made wiki Post Made Community Wiki by Terry Tao