Pythagoras

Father of Numbers:

Those of you in the upper grades and specially those studying mathematics, are sure to have heard of Pythagoras. He was a reputed mathematician and is best known for the Pythagorean Theorem.

Known as the 'Father of Numbers', he was also a well-known scientist, philosopher and founder of the religious movement called Pythagoreanism.

He is often described as the first pure mathematician and is an extremely important figure in the development of mathematics. Yet, we know little about his mathematical achievements mainly due to the code of secrecy maintained by him and his followers and the lack of any of his writings.

Some have even questioned the scope of his contributions to mathematics or natural philosophy. However, it is generally accepted that many of the accomplishments of Plato, Aristotle and Copernicus were based on his ideas.

Life and education

Pythagoras was born on Samos, a Greek island in the eastern Aegean, about 569 BC. His mother was Pythais and his father, Mnesarchus. It is thought that as a young boy, he travelled widely with his father who was a merchant. Pythagoras is also believed to have had two or three brothers.

Although nothing much is known about his childhood, he is said to have gained a sound education at the hands of many well-known philosophers of the day. When he was a young man, he left his native city, to Croton (now Crotone) in southern Italy, to escape the then harsh government.

It is said that one of his teachers who was impressed with Pythagoras' abilities, advised him to go to Egypt and study with the wise priests there. He had made this journey to Egypt around 535 BC. Some of the geometric principles which eventually inspired his formulation of the Pythagorean Theorem may have been learnt during his stint in Egypt.

After an enemy invasion, Pythagoras was taken prisoner and taken to Babylon. Here, he was able to perfect his arithmetic and music and other mathematical sciences taught by the Babylonians. In about 520 BC, Pythagoras left Babylon and returned to Samos.

He left Samos and went to Croton again in about 518 BC. Not content just working with numbers, Pythagoras started reforming the cultural life of Croton; he formed a circle of followers around himself called Pythagoreans. This organisation was in some ways a school, in some ways a brotherhood, and in some ways a monastery.

This cultural centre was governed by a strict code of conduct and was open to both male and female students. They followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. They also observed a rule of silence called echemythia, the breaking of which was punishable by death.

Interest in music

Pythagoras had a keen interest in music and the Pythagoreans were musicians as well as mathematicians. He wanted to improve the music of the time, which he thought was not harmonious enough and too chaotic.

Legend says Pythagoras discovered that musical notes could be translated into mathematical equations after observing blacksmiths at work and listening to the sound made by their equipment. Music was an essential component of the Pythagoreans' life and was even used to cure illnesses; poetry recitations were carried out before and after sleep to aid memory.

One of his major accomplishments was the discovery that music was based on proportional intervals of the numbers one through four.

He also discovered the theory of mathematical proportions, constructed from three to five geometrical solids. Pythagoras (or the Pythagoreans) are also credited with the discovery of square numbers. He was one of the first to think that the Earth was round, that all planets have an axis, and that all the planets travel around one central point.

Pythagoras believed in transmigration, or the reincarnation of the soul into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were influenced by Greek Mythology. He was one of the first to propose that the thought processes and the soul were located in the brain and not the heart.

He was also said to be familiar with and an admirer of, Jewish customs and wisdom. Some have described him as a wonder-worker and a supernatural figure, displaying signs of divinity. Some had believed that he had the ability to travel through space and time, and to communicate with animals and plants.

Towards the end of his life, he fled to Metapontum because of a plot against him and his followers; he died there in about 475 BC.

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The Pythagorean Theorem

It is a theorem in trigonometry that states that in a right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle), c, is equal to the sum of the areas of the squares of the other two sides, b and a, that is, a2+b2=c2.

While this theorem was well known and previously used by the Babylonians, Egyptians and Indians, Pythagoras or his students are thought to have constructed the first proof. There are many ancient references to the facts stated in the Pythagorean Theorem; Egyptian and Chinese tablets and writings show that they knew it.