1. PYTHAGORAS OF
SAMOS
Pythagoras was an influential Greek mathematician
and philosopher, best known for the theory to which
he gave his name.

2. ●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

3. EARLY LIFE
●Born on the island of Samos, off Greece, in the Mediterranean
Sea, Pythagoras was the son of Mnesarchus. Little is known
about his early life. After studying in Greece, he fled to southern
Italy to escape the harsh rule of Polycrates (died c. 522 B.C.E. ),
who came to power about 538 B.C.E. There he began teaching
and soon had a clutch of students who lived a structured life of
study and exercise, inspired by a philosophy based around
mathematics. This circle came to be known as the Pythagoreans.

4. EARLY LIFE
●Pythagoras and his followers became politically powerful in
Croton in southern Italy, where Pythagoras had established a
school for his newly formed sect, or group of followers. It is
probable that the Pythagoreans took positions in the local
government in order to lead men to the pure life that was directed
by their teachings. Eventually, however, a rival group launched an
attack on the Pythagoreans at a gathering of the sect, and the
group was almost completely destroyed. Pythagoras either had
been forced to leave Croton or had left voluntarily shortly before
this attack. He died in Metapontum early in the fifth century B.C.E.

5. PYTHAGOREANS
●The early Pythagoreans were upper middle class and politically
active. They formed a moral elite who strove to perfect their
physical form in this life in order to gain immortality in the next. To
free the soul and achieve immortality, the mortal body had to be
rigorously disciplined to keep it morally pure and free of the base
nature. Until this could be achieved the soul would be repeatedly
reincarnated, or 'transmigrated', until released by accumulated
merit.

6. BELIEFS
●Pythagoreans also believed in the cosmos, which at that time
referred to an idea of a clockwork order and beauty in the whole
universe. While probably believing in classical Greek polytheism,
they maintained a superior divinity, the one, above all others.
They had a number of taboos, including the avoidance of meat
and beans, and lived by a series of rules governing all aspects of
life. In approximately 500 BC, there appears to have been an
uprising against the power of the Pythagoreans. Pythagoras fled
and is thought to have been killed or died shortly afterwards.

7. MATHEMATICAL TEACHINGS
●So great was the Pythagoreans' respect for the "Tetractys of the
Decad" (the sum of 1 + 2 + 3 + 4) that they swore their oaths
(promises) by it rather than by the gods, as was normal during his
day. Pythagoras may have discovered the theorem which still
bears his name (in right triangles [triangle with one angle equal to
90 degrees], the square on the hypotenuse equals the sum of the
squares on the other sides), although this proposal has been
discovered on a writing stone dating from the time of the
Babylonian king Hammurabi (died c. 1750 B.C.E. ). Regardless of
their sources, the Pythagoreans did important work in extending
the body of mathematical knowledge.

8. MATHEMATICAL TEACHINGS
●As a more general outline, the Pythagoreans presented the two
contraries (opposites), Limited and Unlimited, as ultimate
principles, or truths. Numerical oddness and evenness are
equated with Limited and Unlimited, as are one and plurality
(many), right and left, male and female, motionlessness and
movement, straight and crooked, light and darkness, and good
and bad. It is not clear whether an ultimate One, or Monad, was
presented as the cause of the two categories.

9. PYTHAGORAS THEOREM
● His main discovery was the Pythagoras theorem:
●The theorem has numerous proofs, possibly the most of any
mathematical theorem.
●These are very diverse, including both geometric proofs and
algebraic proofs, with some dating back thousands of years.
●The theorem can be generalized in various ways, including higher-
dimensional spaces, to spaces that are not Euclidean, to objects that
are not right triangles, and indeed, to objects that are not triangles at all,
but n-dimensional solids.
●In any right-angled triangle, the square of the hypotenuse is equal to
the sum of the squares of the other two sides

10. DEATH
●Pythagoras's death is unknown. Some say he died in a revolt in
which the meeting place of the Pythagoreans was surrounded
and set to fire, of which only a few survived. Others say the
members formed a bridge using their bodies over the flames to
allow Pythagoras to escape. He fled to Metapontum where he
chose to die at the hands of his enemies rather than trample over
a sacred bean field.