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Mathematics in India

Book Description

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning.

Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition.

**Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface
  6. List of Abbreviations
  7. Chapter One - Introduction
    1. 1.1 Background and Aims of This Book
    2. 1.2 History and South Asia
    3. 1.3 Sanskrit Literature and the Exact Sciences
  8. Chapter Two - Mathematical Thought in Vedic India
    1. 2.1 The Vedas and Mathematics
    2. 2.2 The ŚUlba-Sūtras
    3. 2.3 The Vedas and Astronomy
    4. 2.4 The Jyotisa-Vedānga
    5. 2.5 Vedic India and Ancient Mesopotamia
  9. Chapter Three - Mathematical Traces in the Early Classical Period
    1. 3.1 Numbers and Numerals
    2. 3.2 Astronomy, Astrology, and Cosmology
    3. 3.3 Mathematical Ideas in other Disciplines
    4. 3.4 Mathematics in Jain and Buddhist Texts
  10. Chapter Four - The Mathematical Universe Astronomy and Computation in the First Millennium
    1. 4.1 An Introduction to Geocentric Astronomy
    2. 4.2 Evolution of the Siddhānta and Astronomical Schools
    3. 4.3 Astronomical Calculations in Siddhānta
    4. 4.4 Other Texts for Astronomical Computation
    5. 4.5 Geometric Models in Astronomy
    6. 4.6 The Problem of Origins
  11. Chapter Five - The Genre of Medieval Mathematics
    1. 5.1 Chapters on Mathematics in Siddhāntas
    2. 5.2 The Bakhshālī Manuscript
    3. 5.3 The Ganita-Sāra-Sangraha
  12. Chapter Six - The Development of “Canonical” Mathematics
    1. 6.1 Mathematicians and Society
    2. 6.2 The “Standard” Texts of Bhāskara (II)
    3. 6.3 The Works of Nārāyana Pandita
    4. 6.4 Mathematical Writing and Thought
  13. Chapter Seven: The School of Mādhava in Kerala
    1. 7.1 Background
    2. 7.2 Lineage
    3. 7.3 Infinite Series and other Mathematics
    4. 7.4 Astronomy and Scientific Methodology
    5. 7.5 Questions of Transmission
  14. Chapter Eight - Exchanges with the Islamic World
    1. 8.1 Indian Mathematics in the West
    2. 8.2 Mathematical Encounters in India
    3. 8.3 Influence and Synthesis
  15. Chapter Nine - Continuity and Changes in the Modern Period
    1. 9.1 Individuals, Families, and Schools
    2. 9.2 Contacts with Europe
    3. 9.3 Mathematics and Astronomy, 1500-1800
    4. 9.4 Conclusion
  16. Appendix A - Some Basic Features of Sanskrit Language and Literature
    1. A.1 Elements of Spoken and Written Sanskrit
    2. A.2 The Structure of Sanskrit verse
    3. A.3 The Documentary Sources of Texts
    4. A.4 Meaning and Interpretation Caveat Lector!
    5. A.5 Glossary of Transliterated Technical Terms
  17. Appendix B - Biographical Data on Indian Mathematicians
  18. Bibliography
  19. Index