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This book traces the first faltering steps taken in the mathematical theorisation of infinity which marks the emergence of modern mathematics. It analyses the part played by Indian mathematicians through the Kerala conduit, which is an important but neglected part of the history of mathematics.
Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact begins with an examination of the social origins of the Kerala School and proceeds to discuss its mathematical genesis as well as its achievements. It presents the techniques employed by the School to derive the series expansions for sine, cosine, arctan, and so on. By using modern notation but remaining close to the methods in the original sources, it enables the reader with some knowledge of trigonometry and elementary algebra to follow the derivations. While delving into the nature of the socio-economic processes that led to the development of scientific knowledge in pre-modern India, the book also probes the validity or otherwise of the conjecture of the transmission of Kerala mathematics to Europe through the Jesuit channel.
The book straddles two domains: science and social sciences. It will appeal to those interested in mathematics, statistics, medieval history, history of science and technology, links between mathematics and culture and the nature of movements of ideas across cultures.
Table of Contents
The Social Origins of the Kerala School
The Mathematical Origins of the Kerala School
The Highlights of Kerala Mathematics and Astronomy
Indian Trigonometry: From Ancient Beginnings to Nilakantha
Squaring the Circle: The Kerala Answer
Reaching for the Stars: The Power Series for Sines and Cosines
Changing Perspectives on Indian Mathematics
Exploring Transmissions: A Case Study of Kerala Mathematics
A Final Assessment