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Philosophy of Sciences

2015 year, number 4

Diophantus of Alexandria and Neo-Pythagorean tradition

E.V. Afonasin1,2
1Institute of Philosophy and Law SB RAN, Novosibirsk
2Novosibirsk State University, Novosibirsk
Keywords: Diophantus, new dating, ancient algebra, Neopythagorean arithmetic

Abstract

A curious instance of utilization of algebraic terminology in Hippolytus ( Elenchos I 2, 9-10: dynamis, cubus, dynamocubus , etc.) indicates that a relatively advanced arithmetic originated in works of such mathematicians as Heron and Diophantus, for some reason, aroused interest in Platonic and Pythagorean circles. Indeed, if we were to look for an example of an ideal Pythagorean, Diophantus would certainly qualify: he wrote a book on such a popular Pythagorean subject as polygonal numbers, transformed traditional arithmetic, and created a new theory of number; in a word, he did things a Pythagorean is supposed to do. It is no secret that Pythagorean numerology is not very useful from a mathematical point of view. What if an unknown Pythagorean (Hippolytus source) decided to translate the standard Pythagorean theory into the language of higher mathematics of his time? It is as if asked to define number I were to indulge in axiomatic set theory. Besides, the text has clear implications for the dating of Diophantus. Textual observations allow us to entertain the idea that Diophantus as the philosophus Pythagoricus was known and used in the Neopythagorean and Platonic sources from the second, and, possibly, the first century AD. Moreover, if he, as it seems, authored an introductory work on arithmetic, he may be set in a series with such persons as Eudorus, Cleomedes, Moderatus, Nicomachus, and Theon of Smyrna as a fully fledged contributor to the development of the Neopythagorean movement, perhaps to be placed somewhere between Eudorus and Nicomachus.