Pythagoras
Pythagoras of Samos is often described as the first pure mathematician. He is an
extremely important figure in the development of mathematics yet we know
relatively little about his mathematical achievements. Unlike many later Greek
mathematicians, where at least we have some of the books which they wrote, we
have nothing of Pythagoras\'s writings. The society which he led, half religious
and half scientific, followed a code of secrecy which certainly means that today

Pythagoras is a mysterious figure. We do have details of Pythagoras\'s life from
early biographies which use important original sources yet are written by
authors who attribute divine powers to him, and whose aim was to present him as
a god-like figure. What we present below is an attempt to collect together the
most reliable sources to reconstruct an account of Pythagoras\'s life. There is
fairly good agreement on the main events of his life but most of the dates are
disputed with different scholars giving dates which differ by 20 years. Some
historians treat all this information as merely legends but, even if the reader
treats it in this way, being such an early record it is of historical
importance. Pythagoras\'s father was Mnesarchus ([12] and [13]), while his mother
was Pythais [8] and she was a native of Samos. Mnesarchus was a merchant who
came from Tyre, and there is a story ([12] and [13]) that he brought corn to

Samos at a time of famine and was granted citizenship of Samos as a mark of
gratitude. As a child Pythagoras spent his early years in Samos but travelled
widely with his father. There are accounts of Mnesarchus returning to Tyre with

Pythagoras and that he was taught there by the Chaldaeans and the learned men of

Syria. It seems that he also visited Italy with his father. Little is known of

Pythagoras\'s childhood. All accounts of his physical appearance are likely to be
fictitious except the description of a striking birthmark which Pythagoras had
on his thigh. It is probable that he had two brothers although some sources say
that he had three. 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. One of
the most important was Pherekydes who many describe as the teacher of

Pythagoras. The other two philosophers who were to influence Pythagoras, and to
introduce him to mathematical ideas, were Thales and his pupil Anaximander who
both lived on Miletus. In [8] it is said that Pythagoras visited Thales in

Miletus when he was between 18 and 20 years old. By this time Thales was an old
man and, although he created a strong impression on Pythagoras, he probably did
not teach him a great deal. However he did contribute to Pythagoras\'s interest
in mathematics and astronomy, and advised him to travel to Egypt to learn more
of these subjects. Thales\'s pupil, Anaximander, lectured on Miletus and

Pythagoras attended these lectures. Anaximander certainly was interested in
geometry and cosmology and many of his ideas would influence Pythagoras\'s own
views. In about 535 BC Pythagoras went to Egypt. This happened a few years after
the tyrant Polycrates seized control of the city of Samos. There is some
evidence to suggest that Pythagoras and Polycrates were friendly at first and it
is claimed [5] that Pythagoras went to Egypt with a letter of introduction
written by Polycrates. In fact Polycrates had an alliance with Egypt and there
were therefore strong links between Samos and Egypt at this time. The accounts
of Pythagoras\'s time in Egypt suggest that he visited many of the temples and
took part in many discussions with the priests. According to Porphyry ([12] and
[13]) Pythagoras was refused admission to all the temples except the one at

Diospolis where he was accepted into the priesthood after completing the rites
necessary for admission. It is not difficult to relate many of Pythagoras\'s
beliefs, ones he would later impose on the society that he set up in Italy, to
the customs that he came across in Egypt. For example the secrecy of the

Egyptian priests, their refusal to eat beans, their refusal to wear even cloths
made from animal skins, and their striving for purity were all customs that

Pythagoras would later adopt. Porphyry in [12] and [13] says that Pythagoras
learnt geometry from the Egyptians but it is likely that he was already
acquainted with geometry, certainly after teachings from Thales and Anaximander.

In 525 BC Cambyses II, the king of