Cool answers:
http://math.stackexchange.com/questions/21199/is-dy-dx-not-a-ratio/21209#21209
http://math.stackexchange.com/questions/74347/construct-a-function-which-is-continuous-in-1-5-but-not-differentiable-at-2/74383#74383
http://math.stackexchange.com/questions/21525/mathematical-precise-definition-of-a-pde-being-elliptic-parabolic-or-hyperbolic/21540#21540