Cultural Foundations of Mathematics : The Nature of Mathematical Proof and Transmission of the Calculus From India to Europe in the 16th c. CE

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The volumes of the Project of History of Science, Philosophy and Culture in Indian Civilization commissioned by the Centre for Studies in Civilizations of the Indian Council of Philosophical Research follow multidisciplinary, multi-pronged approaches to discover the main aspects of India’s heritage and their relations to contemporary Indian society. This volume documents how and why the calculus developed in India, over a thousand year period, and was transmitted to Europe in the 16th c., without acknowledgment. To better understand this process, this volume emphasizes the non-universality of present-day formal mathematics—tracing theorem-proving to its theological origins, and highlighting alternative beliefs about logic, proof, and number. A new history and philosophy of mathematics emerges, and is applied to various contemporary issues: mathematics education, computational mathematics, and the extensions of the calculus needed for quantum field theory and shock waves.ContentsPART I THE NATURE OF MATHEMATICAL PROOF Euclid and Hilbert Proof vs Pranama PART II THE CALCULUS IN INDIA Infinite Series and ð Time, Latitude, Longitude, and the Globe Navigation PART III TRANSMISSION OF THE CALCULUS TO EUROPE Models of Information Transmission How and Why the Calculus was Imported into Europe Numbers in Calculus, Algorismus and Computers PART IV THE CONTEMPORARY RELEVANCE OF THE REVISED HISTORY Math Wars and the Epistemic Divide in Mathematics

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C.K. Raju, Ph.D., (Indian Statistical Institute) has taught in the mathematics and statistics departments of the University of Poona (1981–88) before joining C-DAC (Centre for Development of Advanced Computing) to play a key role in building the first Indian supercomputer Param (1988–95).