## Introduction

Pythagoras of Samos (c. 570 – 490 B.C.) was an early Greek Pre-Socratic philosopher and mathematician from the Greek island of Samos.

He was the founder of the influential philosophical and religious movement or cult called Pythagoreanism, and he was probably the first man to actually call himself a philosopher (or lover of wisdom). Pythagoras (or in a broader sense the Pythagoreans), allegedly exercised an important influence on the work of Plato.

As a mathematician, he is known as the “father of numbers” or as the first pure mathematician, and is best known for his Pythagorean Theorem on the relation between the sides of a right triangle, the concept of square numbers and square roots, and the discovery of the golden ratio.

Unfortunately, little is known for sure about him, (none of his original writings have survived, and his followers usually published their own works in his name) and he remains something of a mysterious figure. His secret society or brotherhood had a great effect on later esoteric traditions such as Rosicrucianism and Freemasonry.

## Life

Pythagoras was born on the Greek island of Samos, in the eastern Aegean Sea off the coast of Turkey, some time between 580 and 572 B.C. His father was Mnesarchus, a Phoenician merchant from Tyre; his mother was Pythais, a native of Samos. He spent his early years in Samos, but also travelled widely with his father.

According to some reports, as a young man he met Thales , who was impressed with his abilities and advised him to head to Memphis in Egypt and study mathematics and astronomy with the priests there, which he soon had the opportunity of. He also travelled to study at the temples of Tyre and Byblos in Phoenicia, as well as in Babylon. At some point he was also a student of Pherecydes of Syros and of Anaximander (who himself had been a student of Thales).While still quite a young man, he left his native city for Croton in southern Italy in order to escape the tyrannical government of Polycrates, the Tyrant of Samos (or possibly to escape political problems related to an Egyptian-style school called the “semicircle”which he had founded on Samos).

In Croton, Pythagoras established a secret religious society very similar to (and possibly influenced by) the earlier Orphic cult, in an attempt to reform the cultural life of Croton. He formed an elite circle of followers around himself, called Pythagoreans or the Mathematikoi (“learners”), subject to very strict rules of conduct, owning no personal possessions and assuming a largely vegetarian diet. They followed a structured life of religious teaching, common meals, exercise, music, poetry recitations, reading and philosophical study (very similar to later monastic life). The school (unusually for the time) was open to both male and female students uniformly (women were held to be different from men, but not necessarily inferior). The Mathematikoi extended and developed the more mathematical and scientific work Pythagoras began.

Other students, who lived in neighbouring areas, were also permitted to attend some of Pythagoras’ lectures, although they were not taught the inner secrets of the cult. They were known as the Akousmatikoi (“listeners”), and they focused on the more religious and ritualistic aspects of Pythagoras’ teachings (and were permitted to eat meat and own personal belongings).

Among his more prominent students were the philosopher Empedocles, Brontinus (who may have been Pythagoras’ successor as head of the school), Philolaus (c. 480 – 385 B.C., who has been credited with originating the theory that the earth was not the center of the universe), Lysis of Taras (who is sometimes credited with many of the works usually attributed to Pythagoras himself), Cercops(an Orphic poet), Hippasus of Metapontum (who is sometimes attributed with the discovery of irrational numbers), Zamolxis (who later amassed great wealth and a cult following as a god among the Thracian Dacians) and Theano (born c. 546 B.C., a mathematician, student, and possibly wife or daughter, of Pythagoras).

Towards the end of his life, Pythagoras fled to Metapontum (further north in the Gulf of Tarentum) because of a plot against him and his followers by a noble of Croton named Cylon. He died in Metapontum from unknown causes some time between 500 and 490 B.C., between 80 and 90 years old.

## Work

Because of the secretive nature of his school and the custom of its students to attribute everything to Pythagoras himself, it is difficult today to determine who actually did which work. To further confuse matters, some forgeries under his name (a few of which still exist) circulated in antiquity. Some of his biographers clearly aimed to present him as a god-like figure, and he became the subject of elaborate legends surrounding his historical persona.

The school that Pythagoras established at Croton was in some ways more of a secret brotherhood or monastery. It was based on his religious teachings and was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism, and devote themselves to the mathematics of nature. They also abstained from meat, abjured personal property and observed a rule of silence (called “echemythia”), the breaking of which was punishable by death, based on the belief that if someone was in any doubt as to what to say, they should remain silent.

Pythagoras saw his religious and scientific views as inseparably interconnected. He believed in the theory of metempsychosis or the transmigration of the soul and its reincarnation again and again after death into the bodies of humans, animals or vegetables until it became moral (a belief he may have learned from his one-time teacher Pherecydes of Syros, who is usually credited as the first Greek to teach the transmigration of souls). He was one of the first to propose that the thought processes and the soul were located in the brain and not the heart.

Another of Pythagoras’ central beliefs was that the essence of being (and the stability of all things that create the universe) can be found in the form of numbers, and that it can be encountered through the study of mathematics. For instance, he believed that things like health relied on a stable proportion of elements, with too much or too little of one thing causing an imbalance that makes a person unhealthy.

In mathematics, Pythagoras is commonly given credit for discovering what is now know as the Pythagorean Theorem (or Pythagoras’ Theorem), a theorem in geometry that states that, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Although this had been known and utilized previously by the Babylonians and Indians, he (or perhaps one of his students) is thought to have constructed the first proof.

He believed that the number system (and therefore the universe system) was based on the sum of the numbers one to four (i.e. ten), and that odd numbers were masculine and even numbers were feminine. He discovered the theory of mathematical proportions, constructed from three to five geometrical solids, and also discovered square numbers and square roots. The discovery of the golden ratio (referring to the ratio of two quantities such that the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller, approximately 1.618) is also usually attributed to Pythagoras, or possibly to his student, Theano.

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 (which he originally identified as the Earth, but later renounced it for the idea that the planets revolve around a central “fire”, although he never identified it as the Sun). He also believed that the Moon was another planet that he called a “counter-Earth”.

Pythagoras was also very interested in music, and wanted to improve the music of his day, which he believed was not harmonious enough and was too hectic. According to legend, he discovered that musical notes could be translated into mathematical equations by listening to blacksmiths at work. “Pythagorean tuning” is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2 (a stack of perfect fifths), a system which has been documented as long ago as 3500 B.C. in Babylonian texts, but which is nevertheless often attributed to Pythagoras. He also believed in the “musica universalis” (or the “harmony of the spheres”), the idea that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a kind of symphony.