Pythagoras was a Greek philosopher who lived about 2,500 years ago. He worked in the fields of music and geometry. He also began a religious societry and wrote a general account of the world. His expertise was in the fields of mathametics and astronomy. Not much is known about his life. He waa born on the island of Somos, near Greece and later lived in Crotona, in southern Italy, where he established a religious fraternity whose members were required to abide by the strict rules that he had laid down. His rules seemed quite strange, such as the one that forbade the eating of beans. One of his beliefs was that the souls of people who die transmigrate into other bodies, and sometimes, into the bodies of animals. The fraternity endured until the middle of the 5th century B.C. Although the original purpose of the fraternity was religious rather than political, it became involved in a fierce struggle between the aristocracy and the democracy that was raging in southern Italy. The democratic party gradually superceded that of the religious. The fury that ensued ended in tragedy for the Pythagorean brothers whose meeting places were burned down and destroyed. It is not known if Pythagoras himself perished in this outbreak or whether he died a natural death.
Pythagoras discovered that if one plucks a stretched string, as on a harp, the longer the string, the lower the tone. He also worked out a system of numbers, representing the lengths of the strings, showing that when two tones are harmonious, they sound well together. He later decided that numbers underlie not only music, but everything. In the case of music, his explanations made considerable sense, though in other cases, they made no sense. For instance, he concluded that number 3 representedd marriage and the number 4 represented justice. In geometry, he is best remembered for his theorem, known as the Pythagorean theorem.
In the field of astronomy, Pythagoreans first thought that the earth, as a globe, revolve with other planets, including the sun, around a central fire. They held that the movement of the spheres caused a certain sound of music which they called the "harmony of the spheres."
Pythagoreans adhered to certain mysteries. Prior to membership initiation, one was required to be physically fit. Also obedience, silence, abstinence from food, simplicity in dress and "external goods" were a "must." They believed in immotality and transmigration. One of their philosophies were that proportion, order and harmony of the universe were closely connected with numbers which they considered as the essential character of the universe. They made mathematics an important science on the basis of their system of philosophy, laying the foundation for further developments in geometry. The great mathematical discovery of Pythagoras was the hypotenuse theorem, namely, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.