Astronomy and Mathematics

by

Kim Plofker

• LAST REVIEWED: 27 January 2011
• LAST MODIFIED: 27 January 2011
• DOI: 10.1093/obo/9780195399318-0007

Introduction

“Astronomy” and “mathematics” are names of sciences in the Western intellectual tradition that have no exact counterparts in ancient and medieval India. Their closest equivalents are the Classical Sanskrit śāstras (“treatises” or “disciplines”) of jyotisa (from jyotis, “light,” “luminary,” “celestial body”) and ganita (from the root gan, “to count, enumerate”). But the relationship between these two śāstras is somewhat fluid: ganita in some contexts is considered a subdiscipline of jyotisa, namely the technical computations of mathematical astronomy, while in a broader sense jyotisa as a quantitative discipline is subsumed under ganita or quantitative thought in general. In still other contexts, both words have connotative links to astrology (as did the words “astronomer” and “mathematician” in the premodern West), and in modern South Asia the term jyotisa or “jyotish” refers almost exclusively to astrology. These disciplines grew out of the ancient Vedāṅgas or categories of knowledge that supported the correct performance of Vedic recitation and worship. Their roots are chiefly in the Vedāṅga of jyotisa, which was primarily concerned with the lunisolar calendric computations required for the proper timing of rituals, and which gave its name to the later Classical śāstra incorporating all astral sciences. Some mathematical knowledge was developed in other Vedāṅgas, particularly the Vedāṅga called kalpa which described ritual practice, including geometric manipulations and calculations for constructing brick sacrificial altars. The routines of commerce and government administration as well as foreign scientific traditions also significantly contributed to the body of knowledge on mathematical sciences. The category of jyotisa in Classical śāstras embraced divination by omens and astrology in addition to models and methods for the computations of mathematical astronomy. Nonastronomical mathematics, comprising general arithmetic, geometry, algebra, and other topics that would nowadays be categorized as combinatorics, series, number theory, and so on, was expounded in separate chapters of astronomy treatises or sometimes in separate works. As in other śāstras, technical texts in astronomy and mathematics generally consisted of compact, easily remembered formulas in metrical Sanskrit verse. Commentaries in prose (or occasionally in verse) explained, illustrated, and sometimes demonstrated the formulas. This article will use “astronomy” and “mathematics” more or less interchangeably with jyotisa and ganita respectively, relying on the Sanskrit names when focusing on features unique to the Sanskrit tradition. The citations provided within are limited almost entirely to works either written in English or including full English translations of primary texts. Readers interested in locating published editions of other Sanskrit originals with or without translations should see Bibliographies.

Introductory Works

Most of the published research on Indian mathematics and astronomy treats the subject as a component of the Classical Sanskrit scholarly tradition. Due to historiographic issues that are still not fully resolved (see Historiographic Controversies), many historical summaries treating earlier periods are controversial or outdated. Even brief introductory overviews for the general reader covering the full chronological scope of the subject can be difficult to find. Hayashi 1994, Hayashi 2003, and Yano 2003 provide three readable and accurate short surveys in easily accessible reference works, making them a good starting point for the reader unfamiliar with the field. Pingree 1981 is extremely thorough and detailed for its size; although it supplies only a little general description at the start of each of its sections, it is an indispensable guide to the primary sources.

• Hayashi, Takao. “Indian Mathematics.” In Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Vol. 1. Edited by I. Grattan-Guinness, 118–130. New York: Routledge, 1994.

  A very helpful description of the chief features and development of nonastronomical mathematics.

• Hayashi, Takao. “Indian Mathematics.” In Blackwell Companion to Hinduism. Edited by Gavin Flood, 360–375. Oxford: Blackwell, 2003.

  This essay goes more deeply into some of the source texts and their intellectual context than Hayashi 1994, although it omits some of the broader historical background.

• Pingree, David. Jyotihśāstra: Astral and Mathematical Literature. A History of Indian Literature 6, Fasc. 4. Wiesbaden, Germany: Harrassowitz, 1981.

  This monograph is rather opaque to general readers, being a concise and densely erudite summary description of several hundred primary texts in all eras and fields of Sanskrit astral and mathematical sciences, listed by topic and chronologically within brief sketches of the history of the fields. For combined brevity and comprehensiveness, however, it is unequalled.

• Yano, Michio. “Calendar, Astronomy, and Astrology.” In Blackwell Companion to Hinduism. Edited by Gavin Flood, 376–392. Oxford: Blackwell, 2003.

  Focuses on the Hindu context of these subjects more than the details of their technical content; especially good as an introduction to Indian astrological and calendric concepts.