Chapter 8 - The problem of Pythagorean mathematics

Summary

The first network of Greek mathematics

Before turning specifically to Pythagorean mathematics we need to consider the development of Greek mathematical culture as a whole. We all know the narratives where impersonal continuities replace individuals, for example, “The History of Greek Mathematics.” In fact, Greek mathematics, like most other ancient cultural endeavors, may have been pursued primarily by small networks that did not survive beyond two generations or so. 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 (In Eucl. 65.7–68.4 Friedlein), standardly understood to derive from Eudemus’ history of geometry, and the one constituted by Archimedes, his correspondents, and the authors in the following generation. It is the first network that is relevant to Pythagoreanism.

Proclus’ list includes three names from the archaic era: Thales, Mamercus and Pythagoras. Hippias of Elis, Anaxagoras and Oenopides are brought in based on their mention in Platonic dialogues; next follow Hippocrates of Chios, Theodorus of Cyrene, (Plato himself) and finally: Leodamas of Thasos, Archytas of Tarentum, Theaetetus of Athens, Neoclides, his pupil Leon, Eudoxus of Cnidus (a little later than Leon), Amyclas of Heracleia, Menaechmus (a student of Eudoxus), Dinostratus, his brother, Theudius of Magnesia, Athenaeus of Cyzicus, Hermotimus of Colophon and Philippus of Mende.