I suspect this post on 'mathematical surprises' from Dave Richeson may get passed around a lot:
http://divisbyzero.com/2010/08/18/mathematical-surprises/
He lists a number of varied mathematical discoveries over the years that surprised the math community and offered new perspectives; his commenters chime in with still more examples.
I think this gets at what mathematicians love about their subject: it is full of never-ending surprises out of the blue; unlike the stereotyped image (all too often held by lay people) of math as boring, tedious, routine, cut-and-dry....
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