Clemency Montelle - Sanskrit Astronomical Tables

Sources and Studies in the History of Mathematics and Physical Sciences

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Sources and Studies in the History of Mathematics and Physical Sciences was inaugurated as two series in 1975 with the publication in Studies of Otto Neugebauers seminal three-volume History of Ancient Mathematical Astronomy, which remains the central history of the subject. This publication was followed the next year in Sources by Gerald Toomers transcription, translation (from the Arabic), and commentary of Diocles on Burning Mirrors. The two series were eventually amalgamated under a single editorial board led originally by Martin Klein (d. 2009) and Gerald Toomer, respectively two of the foremost historians of modern and ancient physical science. The goal of the joint series, as of its two predecessors, is to publish probing histories and thorough editions of technical developments in mathematics and physics, broadly construed. Its scope covers all relevant work from pre-classical antiquity through the last century, ranging from Babylonian mathematics to the scientific correspondence of H. A. Lorentz. Books in this series will interest scholars in the history of mathematics and physics, mathematicians, physicists, engineers, and anyone who seeks to understand the historical underpinnings of the modern physical sciences.

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Clemency Montelle and Kim Plofker

Sanskrit Astronomical Tables

Clemency Montelle

Department of Mathematics & Statistics, University of Canterbury, Christchurch, Canterbury, New Zealand

Kim Plofker

Department of Mathematics, Union College, Schenectady, NY, USA

ISSN 2196-8810 e-ISSN 2196-8829

Sources and Studies in the History of Mathematics and Physical Sciences

ISBN 978-3-319-97036-3 e-ISBN 978-3-319-97037-0

https://doi.org/10.1007/978-3-319-97037-0

Library of Congress Control Number: 2018952064

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Contents

The history of computational algorithms, numerical methods, and data analysis has long been understudied in the history of mathematics, particularly outside the area of early modern and modern Western mathematics. Many founders of the modern discipline of history of mathematics in the nineteenth and twentieth centuries shared a professional bias in favor of identifying the essence of mathematics with elegant and rigorous demonstration of abstract propositions, which was viewed by most of their contemporaries as the highest form of mathematical endeavor. They largely disregarded the evolution of more plebeian or mechanical mathematical activities, such as approximating numerical parameters, constructing tables of function values, and optimizing computational performance. It has only recently started to become apparent how much interesting material the pioneers of history of mathematics overlooked when they neglected the arts of number-crunching. The distorting impact of this historiographic bias on our understanding of the development of mathematics has been particularly severe in the case of non-Western mathematical traditions that emphasized computational methods over proof structures.

The historical role of numeric-array tables in texts treating quantitative sciences and the computational methods used to generate such tables have begun to receive increased scholarly attention in the last few decades, particularly from historians of mathematics and astronomy. Edited collections such as Campbell-Kelly et al. () bring together specialized studies on scientific tables in various periods and cultures of inquiry ranging from pre-classical antiquity to the twentieth century and from East Asia to North America.

Our knowledge of the role and nature of numerical tables within scientific traditions is farther advanced in some areas of specialization than in others. For instance, research on construction and use of tables in the Islamic world has benefited from both broad surveys and investigations into specific aspects, but there remains an enormous amount of unstudied and unpublished material: of the approximately 200 extant Islamic astronomical handbook/table texts (zjes), only a handful have been scrutinized in detail. The study of numerical tables in European manuscripts and early printed works is another growth field just beginning to tackle its immense store of resources. Likewise, the use of tables in ancient Mesopotamia, Greece, Egypt, and China has recently been addressed, but on the whole the genre remains extremely understudied.

Like other types of scientific texts, numerical tables in Sanskrit and other Indic languages tend to be more numerous, and even more neglected, than their counterparts in non-Indian textual traditions. Some early Indologists lumped together all Sanskrit astronomical texts as tables, while others distinguished more carefully between tabular and theoretical works but deplored contemporary Indian astronomers preference for the former over the latter. Well into the twentieth century, this disapproving attitude kept the study of Indian exact sciences somewhat on the defensive. Research tended to focus on the many aspects of Sanskrit texts attesting to theoretical rigor, brilliant discoveries, geometric models, and other qualities conforming to the idealized depictions of Hellenistic and early modern European intellectual traditions that shaped modern conceptions of science. Sanskrit treatises with a strongly computational bent, and the creative numerical techniques used to produce them, received far less attention from historians.