Abstract

This chapter turns from Pythagorean religion to Pythagorean science, primarily to mathematics. It shows that the similarities between Oriental calculations and Greek geometry are delusory, while others are perceived only by someone raised on the analytical geometry of Descartes and capable of translating Babylonian problems into the language of geometrical theorems. It then considers the systematic application of deductive proof, which was the most important factor in the formation in ancient Greece of theoretical mathematics on an axiomatic basis. This is followed by a discussion of Pythagoras' mathematics in fourth-century testimonies, Pythagoras as a mathematician, and Hippasus and Pythagorean mathematics of the first half of the fifth century.