Ancient Mathematics

THE PYTHAGOREAN TRADITION
EDITED BY EUGENE AFONASIN, ANNA AFONASINA AND ANDREY SCHETNIKOV


This anthology contains a concise study of an important cultural and philosophical phenomenon of Late Antiquity, usually labeled as the revived Pythagoreanism or Neopythagoreanism, and offers the major works of the Neopythagoreans in a new Russian translation. Of course the “Neopythagoreans” and their contemporaries considered the movement in question as genuine Pythagoreanism: they did not acknowledge a fundamental gap in the tradition and insisted on the existence of an unbroken chain of succession from Ancient Pythagoreanism to the new one. This brought to life numerous pseudoepigraphic writings attributed to such An-cient Pythagoreans as Theano, Lysius, Hipparchus, Philolaus, Archytas and others. The Life of Pythagoras by Porphyry and On the Pythagorean Way of Life by Iamblichus pictured Ancient Pythagoreans as legendary sages, wonder makers and secret educators of humanity, and the image of Pythagoras created in Late Antiquity is still current in popular opinion. The most exemplary description of a Pythagorean sage, Apollonius of Tyana, produced by Flavius Philostratus, de-serves special attention in this connection and still intrigues scholars from the point of view of both the sources used and ideology involved.
Legendary Apollonius and similar propagators of the “Pythagorean way of life” represent just one side of the Neopythagorean revival. An entirely new philosophic movement, also called the Neopythagoreanism, started to develop approximately in this time. Already discernible in the Middle Platonism, it is found among the Neoplatonists in its fully developed form. These philosophers and their “Pythagorean” numerology and complicated metaphysics of the first principles are the main topic of the book.
Unfortunately only a few works of these authors are extant and the greater part of the material we have to deal with is preserved in fragmentary form in later doxographers and commentators. Since no reliable translation of these fragments existed in Russian so far, we deemed it important to fill up this gap and supply the reader with new translations of these interesting texts. A treatise “On the nature of the world and the soul”, ascribed to an ancient Pythagorean Timaios of Locri and counted among the most interesting pseudonymous philosophical works available, is translated and commented in Chapter 4, the fragments of Moderatus and Numenius are found in Chapters 6 and 9; two treatises by Nicomachus (these in arithmetic and harmonics) are translated in Chapter 7, an introductory manual, “Mathematics useful for understanding Plato” by Theon of Smyrna, a Greek mathematician, strongly influenced by the Neo-Pythagorean school of thought, is translated in Chapter 8, while Chapter 10 is dedicated to the Pythagorean numerology, represented by an anonymous treatise Theologoumena arithmeticae (which contains early material, mainly from Anatolius and Nicomachus). In Chapters 1–3 and 5 we adduce a series of relevant extracts from Greek, Judean and Early Christian philosophers as well as the Gnostic literature, analyzed in the context of Religious systems of Late Antiquity. As general introductions to Chapters 6, 7 and 9 we reprint few pages from the famous book by John Dillon The Middle Platonists (Duckworth, 1977; Cornell UP, 19962), dedicated to Moderatus, Nichomachus and Numenius, in our translation (published in St. Petersburg, 2002, corrected). Two articles of fundamental importance, these by Eric Dodds on the origin of the Neoplatonic One (Classical Quarterly 22 [1928] 129–42) and by John Rist on Neopythagoreanism and “Plato’s” Second Letter (Phronesis 10 [1965] 78–81), are translated as attachments to this volume.
The work will be useful for students of the Pythagorean tradition as well as for a wider readership, including those scholars and students who are interested in Ancient philosophy, mathematics and music. The texts are supplemented by indices and bibliography.

Le prologue du Théétète a, depuis longtemps, suscité beaucoup d'attention parmi les historiens du platonisme. C'est qu'il constitue sans aucun doute le texte le plus important afin de déterminer la chronologie du mathématicien Théétète. Le dialogue, tel qu'il a été transmis par les manuscrits byzantins, s'ouvre en effet sur l'évocation, par Euclide de Mégare, de la disparition prochaine du mathématicien. Celui-ci, blessé lors d'une bataille à Corinthe et atteint de dysenterie, est emporté, mourant, à Athènes. Si l'on accepte l'historicité de cette description platonicienne, l'enjeu du prologue apparaît considérable : car la détermination de la date de la bataille évoquée par Platon fournit à la fois un terminus post quem de l'écriture du prologue qui nous est parvenu, et une date précise de la mort de Théétète.