Chapter 6 - The Canonization of Greek Mathematics

Summary

Time for a survey, for a look back. What we may call “the Greek achievement” is all in: Archytas, Archimedes, Ptolemy . . . Which does not mean, of course, that history stopped. At around the third century ce, however, there is a marked shift. “Porphyry and a New Start” is where we begin—an author of the second half of the third century whose works include a Neoplatonist commentary on past mathematical works. To understand this, we need to bring in two contexts. One is “Platonism and the Return of Number,” where we survey the history of Platonism until its remaking as Neoplatonism. This philosophy has mathematics—and especially, number—at its center. From the third century ce onward, practically all pagan philosophy becomes Neoplatonist. (To understand this process, we also note several mathematical works of the imperial era, more focused on number.) The other context, discussed in “Teachers, Commentaries, Books,” is the rise of commentary as the major form of creativity, starting in the third century ce.