YTHAGORAS OF SAMOS, thought to be the son of a merchant, was well traveled and even took up study in Egypt where he obtained the priesthood from the temple at Diospolis.

He would go on to found a philosophical and religious society, the Pythagorean Society, which, by today's terms, would be considered a cult. The society consisted of a leader (Pythagoras), an inner circle (mathematikoi) and an outer circle (akousmatics). The head and the inner circle members lived within the society, had no personal possessions and were vegetarians. The outer circle members only visited during the day and were allowed to own possessions and eat meat as they pleased. Their main beliefs being:

1. Everything from music to the human body to the solar system is mathematical by nature and can be explained by such,
2. Philosophy can be used for spiritual purification,
3. Souls can rise and merge with the divine,
4. Certain symbols have a mystical significance and
5. Brothers of the order should observe strict loyalty and secrecy.

Despite their cult-like nature, they were known for their mutual friendship, unselfishness and honesty. Regardless, the Pythagorean Society, as all religious and philosophical societies before and after, suffered from persecution. For example in 460 BC, their meeting houses were sacked and burned including one particular incident where 50 to 60 of them were surprised and slain.

Aside from his founding of the Pythagorean Society, there is actually very little known about Pythagoras' actual contributions to math. Since none of his writings have survived and his society was communal in nature and prone to secrecy, it is impossible to distinguish his personal work from that of his followers.

The following discoveries have been credited to Pythagoras and the Pythagoreans:

1. The sum of the angles of a triangle is equal to two right angles. Also, the Pythagoreans knew the generalization which states that a polygon with n sides has a sum of interior angles 2n - 4 right angles and a sum of exterior angles equal to four right angles.
2. The Pythagorean Theorem: For a right angled triangle, the square on the hypotenuse is equal to the sum of the squares of the other two sides.
3. Constructing figures of a given area and geometrical algebra
4. Discovery of irrationals or incommensurable
5. Five regular solids or Platonic figures: the cube, the pyramid, the dodecahedron, the octahedron and the icosahedron (the last two are arguably discovered by Theatetus of Athens)
6. In astronomy, Pythagoras recognized that the orbit of the Moon was inclined to the equator of the Earth, and he was one of the first to realize that Venus as an evening star was the same planet as Venus as a morning star.