Little is known of Pythagoras's childhood. Certainly he was well educated, learning to play the lyre, learning poetry and to recite Homer. There were, among his teachers, three philosophers who were to influence Pythagoras while he was a young man: Pherekydes, Thales, and his pupil Anaximander.

Pythagoras founded a philosophical and religious school that had many followers. Pythagoras was the head of the society with an inner circle of followers who lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. The beliefs that Pythagoras held were that reality is mathematical in nature, philosophy can be used for spiritual purification, the soul can rise to union with the divine, certain symbols have a mystical significance, and all brothers of the order should observe strict loyalty and secrecy.

Both men and women were permitted to become members of the Society. In fact several later female Pythagoreans became famous philosophers. The outer circle of the Society lived in their own houses, only coming to the Society during the day. They were allowed their own possessions, and were not required to be vegetarians.

Pythagoras is often described as the first pure mathematician. Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof. Pythagoras believed that all relations could be reduced to number relations.

Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments. In fact Pythagoras made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill.

Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers, perfect numbers etc. However to Pythagoras, numbers had personalities which we hardly recognise as mathematics today. Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly.

Of course today we particularly remember Pythagoras for his famous geometry theorem. Although the theorem, now known as the Pythagoraean theorem, was known to the Babylonians 1000 years earlier, he may have been the first to prove it.

Of Pythagoras's actual work nothing is known. The secrecy practiced by his School makes it distinguish between the work of Pythagoras and that of his followers. Other mathematics attributed to the Pythagoreans are: the sum of the angles of a triangle is equal to two right angles, a polygon with n sides has sum of interior angles (2n–4) right angles and sum of exterior angles equal to four right angles, the existence of irrational numbers, the 5 Platonic solids, solving quadratic equations by geometrical means, and the fact that Venus the evening star was the same planet as Venus the morning star.

Primarily, however, Pythagoras was a philosopher. Pythagoreans held the following philosophical and ethical teachings: the dependence of the dynamics of world structure on pairs of opposites, successive reincarnation in different species until its eventual purification, and the understanding that all existing objects were fundamentally composed of form and not of material substance. In their ethical practices, the Pythagorean were famous for their mutual friendship, unselfishness, and honesty.