The Pythagoreans were fond of numbers, whole numbers to be precise. They believed that everything in the Universe could be expressed in terms of whole numbers and the ratios between them, the fractions. It was one unfortunate Pythagorean, Hippasus of Metapontum, who discovered that this is not the case. In fact, even the simplest of geometrical objects, the length of the diagonal of a square of side length $1$, is an irrational number, namely $\sqrt{2}$.