Pythagoras was born in approximately 582 BCE on the Greek island of Samos. In about 530 BCE, he founded a secret society that was partly scientific and partly religious. The Pythagoreans believed in simplicity and frugality in food, dress, and material possessions, and devoted their lives to philosophical studies. Pythagoras greatly influenced Plato, and thus is a key figure in Western philosophy.
The Pythagoreans made fundamental advances in astronomy, postulating that the earth and other planets are spheres traveling in orbits about the sun.
In mathematics, the Pythagoreans believed in the central importance of numbers, studying the properties of odd and even numbers, prime numbers, and square numbers. The famous Pythagorean theorem (the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides) has been abstracted and generalized to an incredible degree. In probability, the generalization states that the variance of a sum of uncorrelated random variables equals the sum of the variances.