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Pythagoras (582 BC – 496
BC, Greek: Πυθαγόρας)
was an Ionian mathematician
and philosopher, known best for the Pythagorean Theorem.
Bust of Pythagoras
Pythagoras, known as "the father of numbers", made influential contributions to Greek philosophy and religious teaching in the
late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings.
Pythagoras was born on the island of Samos, off the coast of Asia Minor. As a young man he left his native city for Croton in Southern Italy to escape the tyrannical government of Polycrates. Many writers credit him with
visits to the sages of Egypt and of Babylon
before going west; but such visits feature stereotypically in the biographies of Greek wise men, and may express legend rather
than fact.
In any case, Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and forming an
elite circle of followers around himself. Very strict rules of conduct governed this cultural center. He opened his school to men
and women students alike.
According to Iamblichus, the Pythagoreans followed a structured life of common meals, exercise, reading and philosophical study. We may
infer from this that participants required some degree of wealth and leisure to join the inner circle. Music featured as an
essential organizing factor of this life: the disciples would sing hymns to Apollo
together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to
aid the memory.
Pythagoras has the reputation of having taught a doctrine of reincarnation. His other teachings appear framed in pithy sayings, or sumbola, often in
question-and-answer format. Some of these teachings took a simple form: "What is wisest?" "Number"; "What is truest?" "Most men
are bad." Others were more cryptic: "What is the Delphic oracle?" "The tetraktys, in which the Sirens sing." Other sumbola related to
sexual, dietary and other taboos, including the proper way to stir a fire or place one's
shoes before going to sleep.
Later Pythagoreans divided into two camps. The akousmatikoi held to these sumbola as the whole of their
master's teaching. The mathematikoi added research into geometry, musical theory, astronomy, mechanics and other
sciences. The mathematikoi held that the akousmatikoi knew only the outer form of the doctrine, but they
themselves claimed to know the inner as well. The akousmatikoi accused the mathematikoi of adding extraneous
material to the original teaching. Even today, scholars cannot definitively identify the "real" Pythagoreans.
The subsequent biographical traditions of Pythagoras reflect this split: they portray him alternately as a down-to-earth
political reformer, a pioneering scientist, or a wild shaman-figure. For example, all
three major biographers agree that Pythagoras spent time in a cave before leaving Samos. Iamblichus holds that he pursued his
studies of geometry and astronomy there. Porphyry contends that he held cousel
among his followers. But in Diogenes Laertius, Pythagoras
apparently immersed himself in mystical study with the seer Epimenides of
Knossos. The truth no doubt lay somewhere in between, but one cannot always say
exactly where. We can infer from the divergent traditions, however, the immense mystical awe in which an early Greek thinker like
Pythagoras might have held number, and also his immediate impulse to connect this insight with the political world around him.
Other pre-Socratics had similar tendencies, but none took them so far as
Pythagoras.
No texts by Pythagoras survive, although forgeries under his name —- a few of which remain extant — did circulate
in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. And ancient Pythagoreans usually quoted
their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature
of his teaching.
Some consider Pythagoras the pupil of Anaximander and some ancient sources
tell of his visiting, in his twenties, the philosopher Thales, just before the death of
the latter. No account exists 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. Evidence certainly suggests that the Egyptians had advanced further than the Greeks of
their time in mathematics and astronomy, and many scholars now believe that the Egyptians used
the Pythagorean Theorem in some of their architectural
projects before the 6th century BC.
It is sometimes difficult to determine which ideas Pythagoras taught originally, as opposed to the ideas his followers later
added. While he clearly attached great importance to geometry, classical Greek writers tended to cite Thales as the great pioneer of this science rather than Pythagoras. The later tradition of Pythagoras as the
inventor of mathematics stems largely from the Roman period.
Whether or not we attribute the Pythagorean theorem to
Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean
tradition and since no evidence remains of earlier Greek or Egyptian musical theories.
The Pythagoreans used the pentagram (five-pointed star) as an important
religious symbol, referring to it as "health".
Pythagoras also allegedly devised an alternative discrete presentation of geometry, known today as Figurate numbers.
Diogenes Laertius (about 200 AD) quotes Alexander's (about 100
BC) book Successions of Philosophers (and according to Diogenes Alexander had access to a book
called The Pythagorean Memoir) in his account of the construction of pythagorean cosmology (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".
(Note that Diogenes, although one of our only sources for early Greek philosophy, by no means provides reliable evidence.
Among other faults, he habitually recasts older ideas into the language of his own day, very often mangling it in the
process.)
This cosmology also inspired the Arab gnostic Monoimus to combine this system with monism and other influences
to form his own cosmology.
The influence of Pythagoras has transcended the field of mathematics, and the Hippocratic Oath — with its central commitment to First do no harm — has its
roots in the oath of the Pythagorean Brotherhood [1] .
In some European medieval texts the name Pythagoras appears written in Italo-Latinate form as Pitagora.
References
- Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations.
Other texts usually build solely on these three books.
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- Secondary literature:
- Eric Temple Bell, The Magic of Numbers, Dover, New
York, 1991
- Walter Burkert, Science and Lore in Ancient Pythagoreanism
- K. L., Guthrie (Ed.), The Pythagorean Sourcebook and Library, Phanes,
- Grand Rapids, 1987 ISBN
0-933999-51-8
- Dominic J. O'Meara, Pythagoras Revived, Clarendon Press, Oxford, 1989
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