Pythagoras (Island of Samos, current Greece, 572 BC - Metaponto, now defunct, current Italy, 497 BC) Philosopher and Greek mathematician. Although its name is linked to the theorem of Pythagoras and the school founded by it gave an important impetus to the development of mathematics in ancient Greece, the relevance of Pythagoras also reaches the scope of the history of ideas: his thought, still dyed of the mysticism and esotericism of the ancient mystery and oriental religions, it inaugurated a series of themes and motifs that, through Plato, would leave a deep imprint on the Western tradition. Little is known of the biography of Pythagoras that can be considered reliable, since his status as the founder of a religious sect led to the early appearance of a legendary tradition around his person. It seems certain that he was the son of the merchant Mnesarco and that the first part of his life was spent on the island of Samos, which he probably abandoned a few years before the execution of the tyrant Polícrates, in 522 a.C. It is possible that he traveled then to Miletus, to visit later Phenicia and Egypt; In this last country, cradle of esoteric knowledge, Pythagoras could have studied the mysteries, as well as geometry and astronomy. Some sources say that Pythagoras later went to Babylon with Cambyses II, to learn there the arithmetic and musical knowledge of the priests. They also talk about trips to Delos, Crete and Greece before finally establishing their famous school in the city of Crotona, one of the colonies that the Greeks had founded two centuries earlier in Magna Grecia (now southern Italy) , where he enjoyed considerable popularity and power. The community led by Pythagoras ended, plausibly, by becoming an aristocratic political force that aroused the hostility of the Democratic Party, which led to a revolt that forced Pythagoras to spend the last years of his life in the Greek colony of Metaponto, north of Crotona. The Pythagorean community was always surrounded by mystery; It seems that the disciples had to wait several years before being presented to the teacher and always keep strict secrecy about the teachings received. Women could be part of the brotherhood; the most famous of its adherents was Teano, wife perhaps of the own Pythagoras and mother of a daughter and of two children of the philosopher. The philosophy of Pythagoras. Pythagoras left no written work, and to such an extent it is impossible to distinguish the ideas of the teacher from those of the disciples that can only be exposed the thought of the school of Pythagoras. In fact, externally Pythagoreanism seems more like a mystery religion (like Orphism) than a philosophical school; in that sense it was a lifestyle inspired by an ascetic ideal based on the community of goods, whose main objective was the ritual purification (catharsis) of its members. However, such purification (and this is its main singularity with respect to the mystery cults) was carried out through the cultivation of a knowledge in which music and mathematics played an important role. The path to this knowledge was philosophy, a term that, according to tradition, Pythagoras was the first to use in its literal sense of "love of wisdom"; When the tyrant Leontes asked him if he was a wise man, Pythagoras politely replied that he was "a philosopher," that is, a lover of knowledge. Pythagoras in The School of Athens (1511), by Raphael. Pythagoras is also credited with having transformed mathematics into a liberal teaching (without the usefulness, for example, of agrimentary they had in Egypt) by abstractly formulating its results, regardless of the material context in which some of them were already known. This is, in particular, the case of the famous Pythagorean theorem, which establishes the relationship between the sides of a right triangle: the square of the hypotenuse (the longest side) is equal to the sum of the squares of the legs (the short sides that form the right angle). From the practical use of this relationship there are testimonies from other civilizations before the Greek (such as the Egyptian and the Babylonian), but it is attributed to Pythagoras the first proof of the theorem, as well as numerous other advances to his school. The effort to rise to the generality of a mathematical theorem from its fulfillment in particular cases exemplifies the Pythagorean method for the purification and perfection of the soul, which taught to know the world as harmony. By virtue of this, the universe was a cosmos, that is to say, an ordered set in which the celestial bodies kept a harmonic arrangement that made their distances to each other in proportions similar to those corresponding to the intervals of the musical octave; the celestial spheres, when spinning, produced the so-called music of the spheres,