Pythagoras, one of the most famous and controversial ancient Greek philosophers, lived from ca. 570 to ca. 490 BCE. He spent his early years on the island of Samos, off the coast of modern Turkey. At the age of forty, however, he emigrated to the city of Croton in southern Italy and most of his philosophical activity occurred there. Pythagoras wrote nothing, nor were there any detailed accounts of his thought written by contemporaries. By the first centuries BCE, moreover, it became fashionable to present Pythagoras in a largely unhistorical fashion as a semi-divine figure, who originated all that was true in the Greek philosophical tradition, including many of Plato's and Aristotle's mature ideas. A number of treatises were forged in the name of Pythagoras and other Pythagoreans in order to support this view. The Pythagorean question, then, is how to get behind this false glorification of Pythagoras in order to determine what the historical Pythagoras actually thought and did. In order to obtain an accurate appreciation of Pythagoras' achievement, it is important to rely on the earliest evidence before the distortions of the later tradition arose. The popular modern image of Pythagoras is that of a master mathematician and scientist. The early evidence shows, however, that, while Pythagoras was famous in his own day and even 150 years later in the time of Plato and Aristotle, it was not mathematics or science upon which his fame rested. Pythagoras was famous (1) as an expert on the fate of the soul after death, who thought that the soul was immortal and went through a series of reincarnations; (2) as an expert on religious ritual; (3) as a wonder-worker who had a thigh of gold and who could be two places at the same time; (4) as the founder of a strict way of life that emphasized dietary restrictions, religious ritual and rigorous self discipline. It remains controversial whether he also engaged in the rational cosmology that is typical of the Presocratic philosopher/scientists and whether he was in any sense a mathematician. The early evidence suggests, however, that Pythagoras presented a cosmos that was structured according to moral principles and significant numerical relationships and may have been akin to conceptions of the cosmos found in Platonic myths, such as those at the end of the Phaedo and Republic. In such a cosmos, the planets were seen as instruments of divine vengeance (“the hounds of Persephone”), the sun and moon are the isles of the blessed where we may go, if we live a good life, while thunder functioned to frighten the souls being punished in Tartarus. The heavenly bodies also appear to have moved in accordance with the mathematical ratios that govern the concordant musical intervals in order to produce a music of the heavens, which in the later tradition developed into “the harmony of the spheres.” It is doubtful that Pythagoras himself thought in terms of spheres, and the mathematics of the movements of the heavens was not worked out in detail. There is evidence that he valued relationships between numbers such as those embodied in the so-called Pythagorean theorem, though it is not likely that he proved the theorem. Pythagoras' cosmos was developed in a more scientific and mathematical direction by his successors in the Pythagorean tradition, Philolaus and Archytas. Pythagoras succeeded in promulgating a new more optimistic view of the fate of the soul after death and in founding a way of life that was attractive for its rigor and discipline and that drew to him numerous devoted followers.