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An Overview of Cryptography. Think or Thwim » Mathematical Porn.

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Bill the Lizard: Six Visual Proofs. Weierstrass functions. Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere".

Weierstrass functions

Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent. It is also an example of a fourier series, a very important and fun type of series. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x. PatrickJMT.