Pythagoras was one of the first Greek mathematical thinkers. He is known for proving and teaching the Pythagorean Theorem, which says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse (the long side). He lived in the 500s B.C.E., and spent most of his life in the Greek colonies in Sicily and southern Italy. He had a group of followers Who studied with him and taught other people what he had taught them.
The Pythagoreans were known for their pure lives (they did not eat beans, for example, because they believed that beans were not a pure food). They wore their hair long, wore only simple clothing, and went barefoot. Both men and women Pythagoreans were interested in philosophy, but especially in music and mathematics, which they believed were two ways of making order out of chaos. Nichomachus of Gerasa was a Pythagorean of the first and second centuries. His ideas about arithmetic built upon Pythagoras’s ideas of the harmonic sounds of the motions of the planets and the proportional relationships of numbers.