Pythagoras (fl. 530 BCE) must have been one of the world's greatest men, but he wrote nothing, and it is hard to say how much of the doctrine we know as Pythagorean is due to the founder of the society and how much is later development. It is also hard to say how much of what we are told about the life of Pythagoras is trustworthy; for a mass of legend gathered around his name at an early date. Sometimes he is represented as a man of science, and sometimes as a preacher of mystic doctrines, and we might be tempted to regard one or other of those characters as alone historical. The truth is that there is no need to reject either of the traditional views. The union of mathematical genius and mysticism is common enough.
Originally, from Sámos, Pythagoras founded at Kroton (in southern Italy) a society, which was at once a religious community and a scientific school.
English: Animated geometric proof of the Pythagora...
Italiano: Busto di Pitagora. Copia romana di origi...
English: Similar triangles for Pythagoras' theoremSuch a body was bound to excite jealousy and mistrust, and we hear of many struggles. Pythagoras himself had to flee from Kroton to Metapontion, where he died.
School of Pythagoreans was a school of religion and mathematics that was located in Kroton in southern Italy. The Rules of school were: to abstain from beans, not to pick up what has fallen, not to stir the fire with iron, do not look in a mirror beside a light, and practice vegetarianism. Pythagoras regarded himself as semi-divine "There are men, gods, and men like Pythagoras." Pythagorean Society regarded men and women equally. The property was communal. Mathematical discoveries were communal and by association were attributed to Pythagoras himself -- even from the grave. Hence, exactly what Pythagoras discovered personally is difficult to figure out.
The Mathematics of Pythagoras discovered irrationals by...