MATHEMATICIAN

Life
One of the greatest mathematicians of all time, Pythagoras was the son of Mnesarchus and Pythais; he was born in 580 BC on the island of Samos, and died in about 490 BC, probably in Metapontum (southern Italy). His name, according to one tradition, derives from the Pythia, who foretold his birth and his wisdom when asked by Mnesarchus.


Work
Although Pythagoras was indisputably one of the greatest figures in ancient Greece, remarkably little is known of his life and work. This is largely because of the cultivated mystery surrounding the work and teachings of the Pythagorean brotherhood. He was probably a pupil of Pherecydes in Lesbos and of Thales and Anaximander in Miletus. He is known to have spent 22 years in Egypt with the priests of Memphis, Heliopolis and Diopolis. When Egypt was conquered by Cambyses of Persia, Pythagoras was taken to Babylon as a prisoner: there he had the opportunity to meet and talk with Persian magi. Twelve years later he was released, through the good offices of the (Greek) court physician Democedes, and returned to Samos: by this time he was 56 years old. He was not fated to remain there long, however, for Samos was then under the rule of the totalitarian 'tyrant' Polycrates. Pythagoras soon left the island of his birth for Croton, in south Italy, where with a community of friends he founded a religious brotherhood and school. His ideas had a tremendous impact, particularly on the young, and it was not long before he was accused of atheism and corruption of youth, charges of which he was eventually cleared. Even the manner of his death is not certain: one tradition holds that he died in exile at Metapontum, and another that he was killed in an attack on his school by the citizens of Croton, led by Conon. What is certain is that his school in Croton was closed for political reasons, and many of the brotherhood were killed.

His unusual teachings and the austerity of the communal life in his school soon began to generate legends about him. One such story tells of a great voice saluting him ("Hail, Pythagoras!") from the depths of a river he was crossing with some companions; another tells how in Tunisia he saved himself from certain snakebite by first biting (and killing) the snake. He is also said to have been seen talking with his disciples "on the same day and at the selfsame hour" in Metapontum and in Croton.

Disciples were admitted to his school only after a long and difficult novitiate. Candidates had to observe silence, practise abstinence, and be of strong character; they also had to form close friendships with the other students. Pythagoras held that "a friend is an alter ego", and that "friendship is harmonious equality". Maxims were inscribed in the various rooms of the school, sayings such as "take no heed for the future", and "do not walk in the highways" (that is, do not be swayed by the opinion of the mob, but hold worthy of respect only the opinion of your masters). Before retiring for the night, the disciples were required to go over everything they had done or failed to do during the day: "where did I transgress, what did I do badly, what duty did I fail to accomplish?".

The moral teaching of Pythagoras is contained in the 71 lines known as his "golden words. These contain exhortations to respect the gods and one's parents, to abstinence ("let it be your habit to master your belly first of all, and your sleep and your desires and your passions") and to prudence "think before you act, so that you do not act foolishly. It is the mark of an unhappy man to perform and to speak foolishness. Do therefore those things that you will not regret". Pythagoras also believed in the transmigration of souls; this may reflect the influence of Egyptian teachings. He held that the substance of all things was number, and that the Universe came forth out of chaos, through measure and harmony acquiring form: Pythagoras, indeed, was the first to call the universe the "cosmos", meaning "the harmonious order of things". In his view numbers are the very essence of the cosmos, and not merely symbols of quantitative relations; and for this reason they are sacred. The unit (1) symbolises the spirit, the force from which everything comes into being; the dyad (2) indicates the two forms of matter - Earth and Water; the triad (3) manifests time in its three dimensions: past, present and future; and so on. Cosmic phenomena can be understood through numerology, geometry and music. According to Diogenes Laertius "Pythagoras held the unit to be the origin of all things. From the unit came the indefinite duality, with the expression of the unit as matter also. From numbers came points. From points came lines, from which are formed plane figures, and from them solid figures. From these are formed sensible bodies, with the four elements of fire, water, earth and air, that change and through their changing become the cosmos, animate, intelligible, round, with the Earth at its centre". The idea that the earth revolves about its own axis and at the same time about the Sun can probably also be attributed to the Pythagoreans. The rapid spinning of the heavenly spheres creates sounds, and these create harmony. The soul is the harmony of the body, for it preserves some symmetry between the material and the spiritual element in man. The soul has the properties of identity, otherness, rest and motion (the tetraktys, or "fourness", an expression of perfection).

The name of Pythagoras is inseparably associated with his theorem on right-angled triangles ("the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides"), and with the basic multiplication table, showing the products of the first nine numbers.