Pythagoras

Pythagoras (582 BC - 496 BC) 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.

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.