Cultures of Mathematical Practice in Alexandria in Egypt: Claudius Ptolemy and His Commentators (Second–Fourth Century CE)

Claudius Ptolemy’s mathematical astronomy originated in Alexandria in Egypt under Roman rule in the second century CE and held for more than a millennium, even beyond the Copernican theories (sixteenth century). To trace the flourishing of such mathematical creativity requires an understanding of Ptolemy’s philosophy of mathematical practice, the ancient commentators of Ptolemaic works, and the historical context of Alexandria in Egypt, a multicultural city which became a cradle of cultures of mathematical practices and blossomed into the Ptolemaic system and its several related outputs between the second and fourth centuries CE. Ptolemy’s mathematical practice will be explored under three lenses: (a) an examination of the mathematical prose of Ptolemy’s Almagest alongside the corresponding passages in its Alexandrian commentaries; (b) the social, material, and semantic layers of Ptolemy’s mathematics; and (c) the conception of true philosophy in Ptolemy’s theory of knowledge. Examining the history and philosophy of Ptolemy’s mathematical practice in Alexandria (1) shows that Ptolemy’s ideals were usually betrayed by the practitioners of his mathematics and (2) proves that its main aspect is constituted by mathematical knowledge arranged in tabular format, that is the so-called astronomical tables, to which Ptolemy’s mathematics owes its successful legacy.