A large part of my fascination in mathematics is because of some very surprising results that I have seen there.

I remember one I found very hard to swallow when I first encountered it, was what is known as the Banach Tarski Paradox. It states that you can separate a ball x2+y2+z2≤1 into finitely many disjoint parts, rotate and translate them and rejoin (by taking

disjointunion), and you end up with exactly two complete balls of the same radius!So I ask you which are your most surprising moments in maths?

- Chances are you will have more than one. May I request post multiple answers in that case, so the voting system will bring the ones most people think as surprising up. Thanks!

**Answer**

If a function of a complex variable is once differentiable, it’s infinitely differentiable.

**Attribution***Source : Link , Question Author : Community , Answer Author : Community*