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I collected a bunch of examples into one answer here:

What seemingly innocuous results in mathematics require advanced proofs?

Several commenters noted (correctly, I think) that the examples should have been one per answer.

Should I leave this as is, or edit out all but one of the examples, putting the rest into separate answers (some of which will turn out to be duplicates)?

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    $\begingroup$ I am aware that there are a number of users here that do not take kindly to multiple answers by one person; however, I feel that this is definitely a case where a split is appropriate. $\endgroup$ Aug 17, 2017 at 13:47
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    $\begingroup$ One way to address concern about multiple answers from same person is mark all but one answer as community wiki. Once you do that, no body will complain you are farming for the rep. $\endgroup$ Aug 17, 2017 at 14:49
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    $\begingroup$ I think the question should be community wiki. $\endgroup$ Aug 17, 2017 at 22:28
  • $\begingroup$ I tend to agree with Gerry's suggestion of turning it into CW, but I obviously shouldn't do so on a whim. More so, because a moment's reflection reveals to me that I have this "the voting on the answers is all wrong" feeling. IMHO only Jordan Curve Theorem would fit the description. The hairy ball theorem is borderline ok. May be I interpret the question very narrowly, but I thought the question was about results that are intuitively obvious, but hard to prove. The powerset size axiom result might be ok, but the set of people who would have any intuition about it hardly includes laymen. $\endgroup$ Aug 18, 2017 at 6:34
  • $\begingroup$ Anyway, I also agree that one theorem per answer would be better here. $\endgroup$ Aug 18, 2017 at 6:35

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