Ancient Sanskrit Mathematics: An Oral Tradition and a Written Literature

Abstract

PIERRE-SYLVAIN FILLIOZAT ANCIENT SANSKRIT MATHEMATICS: AN ORAL TRADITION AND A WRITTEN LITERATURE The originality of India's mathematical texts is a consequence of the refined culture of the scholars who produced them. A few examples display clearly some salient features of the habits of exposition and the methods of thought of ancient and medieval Indian mathematicians. The attitude of the traditional learned man, called " pandit " , is the same, whether he works on literary or technical matter. Propensity to orality, use of memory, brain work are his specific qualities. Composition in verse form, use of synonymous words, metaphorical expression, which are unexpected processes for the exposition of technical matter, have been the rule in all the vast Sanskrit mathematical literature. The present article analyses a technique of memorization of the text of the Vedas, the earliest exposition of geometry rules in the context of Vedic rites of building brick altars, the numeration system, the arithmetical and geometrical concept of square. India's mathematical texts are highly original in more than one way: not only do they embody original research methods, they also emerge from a refined culture with which every scholar was deeply imbued. When one examines a Sanskrit scientific text, it is proper not to forget the Indian environment of the author, even if the contents of his work consist of positive knowledge existing also in other civilizations at the same time. The purpose of this article is to draw attention to the intellectual background of ancient and medieval mathematicians. A salient feature is that in ancient times they appear to have been working in an environment of pure orality with original intellectual activities, memorization etc. In the period that followed they worked in an environment where the habits of orality were maintained and the tool of writing was used. We will consider briefly these intellectual habits and give a few examples of mathematical expositions. Indian mathematicians of ancient and early medieval periods whose works have come down to us can be defined as Sanskrit pandits (pan . d . ita " learned man "). 1 What this means is that they underwent an intensive training in handling Sanskrit language, literary com-position and in practicing several intellectual disciplines dealing with language, literature and reasoning. Whatever may be his special field, every pandit possesses a common stock of knowledge in grammar (vy¯ akaran . a), exegesis (m¯ ım¯ am . s¯ a) and logic (ny¯ aya). Thanks to that, he is endowed with a sharp linguistic awareness, equipped with a rich store of potential resources of expression, and has at his disposal a number of heuristic tools. In addition the pandit's education aims at improving the natural faculties of speech and memory.