CHAPTER 3 – The Pythagoreans

TLDR: In this paper, the authors focus on the Pythagoreanism of the late fifth and early fourth centuries, and the importance of Pythagoreans in the history of mathematics and the divine.

Abstract: This chapter focuses on the Pythagoreanism. The place of Pythagoras in the history of mathematics and the divine is well known. There are other people; “Pythagoreans,” were active in the late fifth and early fourth centuries. The most important of these were, apparently, Philolaus and Archytas. They did not suffer the fame of Pythagoras and thus the truth concerning them is somewhat easier to sift from the accretion of later legends. The historical significance of Pythagoreans lies precisely in this: that they were important for Plato and for Aristotle. It is clear that Plato and Aristotle opportunistically changed the meaning of the Pythagorean sources available to them. Plato and Aristotle perceived an affinity between a group of thinkers whom they associated with Pythagoras. They further saw in this group something useful for their own philosophy. To Plato, the usefulness was in the encouragement of a kindred spirit; to Aristotle, the usefulness was in the warning of a philosophical pitfall. The place of this comment is significant: in Aristotle's account, the Pythagoreans immediately preceded Plato, whose philosophy is explained through a mixture of influences from previous thinkers, mainly, that of the Pythagoreans.