The history of Pythagoreanism is littered with different and incompatible interpretations, to the point that Kahn (1974) suggested that, instead of another thesis on Pythagoreanism, it would be preferable to assess traditions with the aim of producing a good historiographical presentation. This almost fourty-year-old observation by Kahn, directs the author of this book towards a fundamentally historiographical rather than philological brand of work, that is, one neither exclusively devoted to the exegesis of sources such as Philolaus, Archytas or even of one of the Hellenistic Lives nor even to the theoretical approach of one of the themes that received specific contributions from Pythagoreanism, such as mathematics, cosmology, politics or theories of the soul. Instead, this monograph sets out to reconstruct the way in which the tradition established Pythagoreanisms image, facing one of the central problems that characterizes Pythagoreanism more than other ancient philosophical movements: the drastically shifting terrain of the criticism of the sources. The goal of this historiographical approach is to embrace Pythagoreanism in its entirety, through - and not in spite of - its complex articulation across more than a millennium.