![]() ![]() Our purpose on the present occasion is to evaluate some ideas the biographers of late antiquity held about the origins of European thought. Keywords: Diophantus, new dating, ancient algebra, Neopythagorean arithmetic. 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. Textual observations allow us to entertain the idea that Diophantus the philosophus Pythagoricus, was known and used in the Neopythagorean and Platonic sources from the second, and, possibly, the first century AD. Besides, the text has clear implications for the dating of Diophantus. What if an unknown Pythagorean (Hippolytus’ source) decided to translate the standard Pythagorean theory into the language of the higher mathematics of his times? It is as if asked to define number I were to indulge in axiomatic set theory. ![]() It is no secret that Pythagorean numerology is not very useful from a mathematical point of view. 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. 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 the works of such mathematicians as Heron and Diophantus, for some reason, aroused interest in Platonic and Pythagorean circles. Wiesbaden: Harrassowitz Verlag (in English), 2016, pp. Eugene Afonasin, ‘Pythagorean numerology and Diophantus’ Arithmetica (A note on Hippolytus’ Elenchos I 2)’, Pythagorean knowledge from the Ancient to the modern world, ed. ![]()
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