Description: Not only the sign for zero, but also the binary number system, the ideas of metarules, algebraic transformation, recursion, hashing, mathematical logic, formal grammars, and high level language description arose first in India. Indian mathematical science had already reached dizzying heights about 2,500 years ago by the time of Panini and Pingala, considered by tradition to have been brothers. Panini's grammar for Sanskrit, which is equivalent in its computing power to the most powerful computing machine, has not yet been matched for any other language, while Pingala described the binary number system. This classic book of contributions by the leading scholars in the world presents an overview of these seminal contributions to computer science. It also includes chapters on models and computation in astronomy and cognitive science.

The material in this book presents an introduction to the Indian contributions to the science of computing. The book starts with an overview of Indian science. The next three chapters deal with the description of binary numbers, the Katapayadi notation and its equivalence to hashing that is used in computer systems, and the Panini-Backus form to describe a high-level computer language based on the ideas of the great grammarian Panini. The next two chapters describe some technical aspects of Panini's grammar and Indian logic. The Paninian structure (5th century BCE) has been shown to be equivalent to the Turing machine. The rise of mathematical logic in India took place centuries before its rediscovery in Europe. The next chapter shows how one needs ingenuity in decoding Indian texts. It is shown that Indian myths represent information regarding the motions of the planets. The last two chapters deal with cosmology and cognitive science.

This book sheds light on the variety of mathematical cultures in general. To do so, it concentrates on cultures of computation and quantification in the ancient world, mainly in ancient China, South Asia, and the Ancient Near East and offers case studies focused on numbers, quantities, and operations, in particular in relation to mathematics as well as administrative and economic activities. The various chapters focus on the different ways and contexts of shaping numbers and quantities, and on the procedures applied to them. The book places special emphasis on the processes of emergence of place-value number systems, evidenced in the three geographical areas under study All these features yield essential elements that will enable historians of mathematics to further capture the diversity of computation practices in their contexts, whereas previous historical approaches have tended to emphasize elements that displayed uniformity within “civilizational” blocks. The book includes editions and translations of texts, some of them published here for the first time, maps, and conventions for editions of ancient texts. It thereby offers primary sources and methodological tools for teaching and learning. The volume is aimed at historians and philosophers of science and mathematics, historians of the ancient worlds, historians of economics, sinologists, indologists, assyriologists, as well as undergraduate, graduate students and teachers in mathematics, the history and philosophy of science and mathematics, and in the history of ancient worlds.

This volume traces back the history of interaction between the “computational” or “algorithmic” aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America.

This volume consists of a collection of articles based on lectures given by scholars from India, Europe and USA at the sessions on 'History of Indian Mathematics' at the AMS-India mathematics conference in Bangalore during December 2003. These articles cover a wide spectrum of themes in Indian mathematics. They begin with the mathematics of the ancient period dealing with Vedic Prosody and Buddhist Logic, move on to the work of Brahmagupta, of Bhaskara, and that of the mathematicians of the Kerala school of the classical and medieval period, and end with the work of Ramanaujan, and Indian contributions to Quantum Statistics during the modern era. The volume should be of value to those interested in the history of mathematics.

Discusses the methods of computation developed in various civilizations around the world, from prehistoric times up until the end of the Roman Empire.

In this pathbreaking book, the authors show that the ancient Indians were no primitives but possessed a high spiritual culture, which not only influenced the evolution of the Western world in decisive ways but which still hs much to teach us today. India's archaic spirituality is codified in the rich symbols, metaphors and myths of the magnificent Rig-Veda, which is shown to be much older than has been widely assumed by scholars. The present book also unravels the astonishing mathematical and astronomical code hidden in the Vedic hymns. Anyone interested in ancient cultural history, India, archaeo-astronomy or spirituality will find this well researched and cross-cultural work spellbinding and enriching.