The concept of number was the foundation for the cosmology of the Pythagoreans. Furthermore, the ratios through which these numbers could be expressed lent a teleological harmony to that cosmology. Hence, the discovery of numbers which could not be put into ratio, incommensurable numbers, must have been quite scandalous. We shall discuss this discovery in terms of geometry and factorization of integers and witness the legend surrounding it. This talk will be entirely accessible to any philosophy or mathematics student.