Pythagoras ( 582BC - 500 BC), was a Greek philosopher and mathematician. Born on the island of Sámos, Pythagoras was instructed in the teachings of early Ionian philosophers including Thales, Anaximander, and Anaximenes. Pythagoras is said to have been driven from Sámos because of his disgust for the tyranny of Polycrates. About 530 BC, after leaving Sámos, Pythagoras settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. This movement emphasized the study of mathematics as a means to understanding all relationships in the natural world, and it was taught by Pythagoreans, the followers and believers of Pythagoras. The philosophy of Pythagoras is known only through the work of his disciples. .

BASIC DOCTRINES:-.

The Pythagoreans adhered to certain mysteries, similar in many.

ways to that of Orphism. These included obedience and silence, doing without food, simplicity in dress and possessions, and the habit of frequent self-examination. The Pythagoreans also believed in immortality and in the transmigration of souls. Pythagoras himself was claimed to have said that he had once been Euphorbus, a warrior in the Trojan War, and that he had been permitted to bring into his earthly life the memory of all his previous existences.

ASTRONOMY:- .

The astronomy of the Pythagoreans marked an important advance in ancient science, for they were the first to consider the Earth as a globe revolving along with the other planets around a central fire (the sun). They explained the arrangement of things as bodies in a single sphere of reality, moving according to a numerical scheme. .

THEORY OF NUMBERS:- .

Among the mathematical investigations carried on by the Pythagoreans were their studies of odd and even numbers and of prime and square numbers, all essential in number theory. From this standpoint they produced the concept of number, which became for them the ultimate principle of all proportion, order, and harmony in the universe.