The problem of Pythagorean mathematics

Abstract

This chapter considers the development of Greek mathematical culture as a whole, and turns specifically to Pythagorean mathematics. A significant part of the Greek creative achievement in pure mathematics may be assigned to two such networks: the one found in Proclus' summary of early Greek mathematics, standardly understood to derive from Eudemus' history of geometry, and the one constituted by Archimedes, his correspondents. Proclus list includes three names from the archaic era: Thales, Mamercus and Pythagoras. Archytas was a major mathematician as well as a Pythagorean. Some people Aristotle identified as Pythagoreans engaged in the systematic analogy between mathematical terms (numerical and musical) and other, cultural and physical phenomena. Certain ideas, or even members, are shared between groups and so the history of culture becomes a network of networks. The group of south Italian Pythagoreans was interested in pursuing analogies based on mathematical concepts, especially those of music and number.