Pythagoras (582 BC - 496 BC, Greek: Πυθαγορας) was a Greek mathematician and philosopher, known best for the Pythagorean Theorem.
Pythagoras, "the father of numbers," was born on the island of Samos off the Greek coast. At a very early age he travelled to Mesopotamia and Egypt where he undertook his basic studies and eventually founded his first school. Political unrest subsequently necessitated a move to Croton in Southern Italy where he founded his second school. The doctrines of this cultural center were bound by very strict rules of conduct. His school was open to men and women students alike, and discriminatory conduct was forbidden. His students included those of all races, colours, religions, and financial or social standing.
Pythagoras as portrayed on Roman coins from Samos
History has documented that the doctrines of the Pythagorean school have had a profound effect on philosophy throughout the ages - even to the present day. Pythagoras believed that mathematics could exist without music or astronomy but mathematical principles were universal and implicit in all things; thus nothing could exist without numbers. His teachings encompassed not only the investigation into the self but into the whole of the known universe of his time. Pythagoras is widely regarded as the founder of modern mathematics, musical theory, philosophy and the science of health (hygiene).
There are no known surviving texts by Pythagoras, but he founded one of the most influential and devoutly followed schools in pre-Socratic Greek thought.
Pythagoras is sometimes considered to be the pupil of Anaximander and is reputed by very early sources to have visited Thales in his twenties, just before Thales died. There is no account of the specifics of the meeting, other than the report that Thales recommended that Pythagoras travel to Egypt in order to further his philosophical and mathematical training. There is certainly evidence that the Egyptians had advanced further than the Greeks of their time in mathematics and astronomy and it is now widely believed that Egyptians used the Pythagorean Theorem in some of their architectural projects before the 6th century BC.
It is sometimes difficult to determine which ideas are original to Pythagoras and which are latter additions by his followers. However, there is general agreement that Pythagoras either developed the Pythagorean Theorem himself or at the very least introduced it to Greek thought. In addition to the Pythagorean Theorem, it there is general agreement that the numerical ratios which determine the musical scale trace back to a discovery by Pythagoras himself, since this plays a key role in many other areas of the Pythagorean tradition, and since there is no evidence of earlier Greek or Egyptian musical theories.
The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans. It was called "health".
A legend exists that Pythagoras was a pupil of Thales, founder of synthetic geometry and of the postulational (axiomatic) method in mathematics. Pythagoras is also said to have devised an alternative discrete presentation of geometry know today as Figurate numbers.
Diogenes Laertius (about 200 BC) quotes Alexanders (about 100 BC) book Successions of Philosophers (and according to Diogenes Alexander has access to a book called The Pythagorean Memoir) in his account of how the pythagorean cosmology was constructed (Diogenes Laertius, Vitae philosophorum VIII, 24):
The principle of all things is the monad or unit; arising from this monad the undefined dyad or two serves as material substratum to the monad, which is cause; from the monad and the undefined dyad spring numbers; from numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four, fire, water, earth and air; these elements interchange and turn into one another completely, and combine to produce a universe animate, intelligent, spherical, with the earth at its centre, the earth itself too being spherical and inhabited round about. There are also antipodes, and our ‘down' is their ‘up'.
This cosmology also inspired the arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.
In some European medieval texts his name is written as Pitagora.