Question

The Weierstrass function is particularly intriguing, as it's a function that's everywhere continuous, but nowhere differentiable.
$f(x)= \sum_{n=0} ^\infty a^n \cos(b^n \pi x)$
where 0<a<1, and b is a positive odd integer such that $ab > 1 + \frac{3\pi}{2}$.
It challenges the notion that, just because a function is continuous, it must also be differentiable in most places, which I think is pretty cool.