Pappus Reborn : Pappus of Alexandria and the Changing Face of Analysis and Synthesis in Late Antiquity.

Abstract

Despite the recent interest in Pappus of Alexandria,the late antiquarian mathematician remains an enigma in the history of mathematics. Only a handful of chapters and fragments of his seminal work, the Collection have been translated into English and there has been little effort to reveal the common mathematical threads therein. To correct this stasis and move Pappian studies into the exploratory stage, I approached the Collection with three questions designed to remove the historiographical biases and avoid the missteps that have persisted over the five-hundred years since Commandino's estate published the first Latin translation. The first question is whether an improved understanding of late antiquity Alexandria and its intellectual environs offer greater insight into Pappus' mathematical style. The second is whether Pappus' infamous exposition on analysis and synthesis from Book 7 of the Collection can be reconciled with propositions from the same book. My final question is that after the reconciliation of proposition and exposition in Book 7, what are the consequences for other books in the Collection that contain otherwise unacknowledged instances of analysis and synthesis? More specifically, will we find consistency between Books 7, 3, and most surprising of all, 2. What is revealed through these questions is the problem modern scholars have with Pappus was never actually about his ability but rather the interference of pedagogy in a field where it is least desired: advanced geometry. Pappus demonstrated thoroughly in Books 2 and 3 that his knowledge of analysis and synthesis was more nuanced than he has been given credit for, involving the social practice of mathematics in Alexandria and the application of arithmetic within a supposedly geometrical method.