Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. Supposedly, he tried to use his teacher's famous theorem a^2 + b^2 = c^2 to find the length of the diagonal of a unit square.
This revealed that a square's sides are incommensurable with its diagonal, and that this length cannot be expressed as the ratio of two integers. The other Pythagoreans believed dogmatically that only positive rational numbers could exist.
They were so horrified by the idea of incommensurability, that they threw Hippassus overboard on a sea voyage, and vowed to keep the existence of irrational numbers an official secret of their sect.
Imagine getting drowned for discovering irrational numbers. It's probably one of the stupidest things to have ever happened in history...
