I'm not sure if this is the most, but Cantor's Diagonal Argument[1] is the first that comes to mind, probably even more as an example of a creative approach tha

I'm not sure if this is the most, but Cantor's Diagonal Argument[1] is the first that comes to mind, probably even more as an example of a creative approach than for its implications (although those are pretty huge too). Charles Petzold's "Annotated Turing" has a great run down of this and a bunch of the other mind-blowing things that came out of math in the late 19th/early 20th centuries. [1] http://en.wikipedia.org/wiki/Cantors_diagonal_argument http://en.wikipedia.org/wiki/Cantors_diagonal_argument