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"He formed a school in the city of Samos, the 'semicircle' of Pythagoras, which is known by that name even today, in which the Samians hold political meetings. They do this because they think one should discuss questions about goodness, justice and expediency in this place which was founded by the man who made all these subjects his business. Outside the city he made a cave the private site of his own philosophical teaching, spending most of the night and daytime there and doing research into the use of mathematics" Iamblichus (3rd Century, A.D.)
Pythagoras is a pertinent figure in the development of Mathematics, yet he is a mysterious figure. The society that he led, half religious and half scientific, followed a code of secrecy and it leaves us parched with relatively little knowledge of his mathematical achievements and his persona. Though historians have laboriously gathered events of his life and reconstructed his story. Today we know him as the Father of Geometry, who had hypothesized "The Pythagoras Theorem." As a child Pythagoras spent his early years in Samos but travelled extensively with his father. From his biographical accounts, we find that the he was well educated, learning and reciting poetry, probably Homer, and learning to play the lyre. Chaldaeans and the learned men of Syria taught him in Tyre. However, the prominent figure in his life, assumed to be his teacher was Pherekydes. Thales and his pupil Anaximander also played a vital role in introducing him to mathematical ideas and astronomy they lived in Miletus.
Thales encouraged him to travel to Egypt and gain knowledge on these subjects. While, Anaximander lectured exclusively on geometry and cosmology, unaware of the future; his ideas would influence Pythagoras's remarkable journey in the educational field.
In about 535 BC Pythagoras went to Egypt, when authoritarian Polycrates seized control of the city of Samos. However, he was refused admission to all the temples except the temple at Diospolis where he was accepted into the priesthood after completing the rites necessary for admission. In 525 BC Cambyses II, the king of Persia invaded Egypt along with Polycrates. Upon wining the battle, Cambyses captured Pythagoras and took him Babylon. The deaths of these rulers encouraged Pythagoras to return to his native birthplace. He founded a school and called it the semicircle. And, embarked upon a journey to Crete, to study the system of laws. Being dragged in diplomatic and political missions, and his teachings were not regarded aptly. Pythagoras left Samos and went to southern Italy in about 518 BC. He commenced a philosophical and religious school in Croton (located on the east of southern Italy). He led the society with an inner circle of followers known as mathematikoi. They possessed no personal materials, obeyed a strict code of conduct, were vegetarians and settled in the Society premises. Both men and women were given equal opportunity and were taught by Pythagoras on the following beliefs:
1. Reality is mathematical in nature, at its deepest level.
2.
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Philosophy can be used for spiritual purification.
3. The soul can rise to union with the divine.
4. Certain symbols have a mystical significance, and
5. All brothers of the order should observe strict loyalty and secrecy.
And, there were people who were keenly interested in Pythagoras teachings, however they equally desired a life with possessions, family and food. These fellow beings were admitted to an outer circle referred as akousmatics. His school practised secrecy and communalism making it difficult to distinguish between the work of Pythagoras and his followers. It is important to note, that Pythagoras was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof. And, they were not a mathematics research group unlike a modern university or other institutions. Phythagorus made outstanding contributions to mathematics. He believed relationships could be reduced to numbers. Aristotle commented: "The Pythagorean having been brought up in the study of mathematics, thought that things are numbers and that the whole cosmos is a scale and a number." This abstraction originated from his observations in music, mathematics and astronomy. Pythagoras noticed that upon vibrating the Lyre strings melodic intonations were produced, because the ratios of the lengths of the strings were whole numbers, and that these ratios could be extended to other instruments. Indeed, he made a remarkable contribution to the mathematical theory of music, which is still used today. Mathematics would have not been accessible, if it was not for Pythagoras who introduced the properties of numbers (even and odd numbers, triangular numbers, perfect numbers, whole numbers) to our contemporary society. Pythagoras is exclusively commemorated for his contribution in Geometry - The Pythagoras Theorem - for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. Proclus, the last major Greek philosopher, who lived around 450 AD, wrote: "Pythagoras transformed the study of geometry into a liberal education, examining the principles of the science from the beginning and probing the theorems in an immaterial and intellectual manner: he it was who discovered the theory of irrational and the construction of the cosmic figures." The contributions of Pythagoras in the field of Geometry, Astronomy and Mathematics,
include:
1. Discovery of irrationals. Due to his belief that universe is constructed of numbers, he hypothesized the hypotenuse of an isosceles right-angled triangle had a length corresponding to a number.
2. Constructing figures of a given area through geometrical algebra. He solved equations a (a - x) = x2 by geometrical means.
3. The sum of the angles of a triangle is equal to two right angles. His school of thought conjectured a polygon with n sides has sum of interior angles 2n - 4 right angles and sum of exterior angles equal to four right angles.
4. The five regular solids.
It is contemplated that Pythagoras knew how to construct the first three but his followers constructed the latter two.
5. Pythagoras taught that the Earth was a sphere at the center of the Universe. He acknowledged the Moon's orbit was inclined towards the Earth's equator. And, the first deep thinker to comprehend Venus was the same planet seen in the evening and morning sky.
In addition to being a philosopher and mathematician, Pythagoras believed in ethical practice related to mutual friendship, altruism and honesty. The Pythagorean Society expanded rapidly after 500 BC, became politically active and was segmented into factions. In 460 BC the Society was violently suppressed, Pythagorean's were murdered and meeting houses burned. In 508 BC Pythagoras escaped to Metapontium and committed suicide, because of his inadequateness to dealing with political events that brought a heavy penalty in form of attack and destruction of his society at Croton.
Plato writes:
"Presiding, like Pythagoras, over a band of intimate disciples who loved him for the inspiration of his society and the way of life which the Pythagoreans called after their founder and which to this day distinguishes them from the rest of the world."