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Apr 28, 2011 at 14:29 comment added Charles Staats This may fall under the Ramsey theory answer, but the fact that a random, countably infinite graph has its isomorphism class determined with probability one (the Rado graph) seems like it might qualify.
Apr 28, 2011 at 13:09 comment added Steven Gubkin See also mathoverflow.net/questions/6707/… and mathoverflow.net/questions/5357/…
Apr 28, 2011 at 9:59 answer added Simon Lyons timeline score: 2
Apr 28, 2011 at 9:51 answer added Steve Huntsman timeline score: 0
Apr 28, 2011 at 9:47 answer added Steve Huntsman timeline score: 3
Apr 28, 2011 at 9:24 answer added John Stillwell timeline score: 9
Apr 28, 2011 at 9:01 answer added Chris Heunen timeline score: 5
Apr 28, 2011 at 9:00 comment added S. Carnahan It looks like you might be interested in universality phenomena. T. Tao has written a nontechnical article: terrytao.wordpress.com/2010/09/14/…
Apr 28, 2011 at 8:00 comment added Roland Bacher It seems to me that the unexpected is often a hallmark of good mathematics. Obvious (and technically easy) results are called exercices.
Apr 28, 2011 at 7:07 answer added zeb timeline score: 1
Apr 28, 2011 at 6:27 comment added Qiaochu Yuan I'm not sure I understand the distinction between structure where it wasn't expected and structure that seems to "arise from a vacuum." Could you give some more examples or non-examples?
Apr 28, 2011 at 5:52 history asked Ramsey CC BY-SA 3.0