Zero and Pi: Symbols of Mathematical Spirit

The book, divided into two major parts, discusses the evolution of the concept and symbols of zero and the history of pi. Both the topics are discussed from the Neolithic Age to the nineteenth century. The book also clears the assumption that Johann Heinrich Lambert (AD 1761) only invented the irrationality of pi by crediting Lambert jointly with André Marie Legendre (AD 1794). Part 1, consisting of six stages spread in six chapters, meets a challenge to the authors as eminent scholars of the history of mathematics have diverse opinions based on conjectures. This part primarily discusses how the symbol O, in the Vedic religious practices, considered a replica of the universe prescribed for meditation on the unknown Brahman (conceived of as the space supreme in the Upanishads), was later transcended to the symbol of an unknown quantity in mathematics along with a dot for zero in an arena of atheism. It also highlights how the zero notation and the decimal system of Indian numerals embellished with the algebraic thoughts of Brahmagupta passed on to China and Europe via Arabia. Topics in this part have traced the development from the origin to the final form as seen today after the western practice and try to put an end to the long-standing debate over history. Appendices contain the Sanskrit verses (transliterated with meanings into English) along with the essential mathematical deduction referred to in the body of the part to help the reader to have a better understanding. Part 2 speaks of a novel idea of unveiling the nature of pi interwoven with threads of historical ups and downs in the world scenario. This part, containing five chapters, collects all available up-to-date data in every field of history to make the presentation complete in all respects. This part discusses the origin of the definition of pi as the rim of a wheel is thrice its diameter at the Indus Valley in the fourth millennium BC. This part also discusses the enlightenment of China in circle-squaring (classical method), Indian mathematics with astronomical knowledge along the Buddhist channel, and India’s discovering circumference/diameter as a non-Euclidean number.

Table of Contents:
Introduction.- Evolution of the Concept and Symbol of Śunya.- The Symbol O of Monism to Atheists, A Dot for Zero.- Gupta Period: A Turn in the History of Śūnya.- Śūnya: Brahmagupta and Bhāskarācārya’s Thought.- Ramification of the Indian Concept of Void/Sūnya.- Introduction.- The Descriptive Geometrical stages.- Identification of π Analytically.- Contextual Topics on Mathematics (A looking back to the old days).- Historical Retrospect.

About the Author :
Amalkumar Mukhopadhyay is an active researcher in Indian astronomy and mathematics. He acted as the resource person in geometry in workshops arranged by the State Council of Education, Research and Training and the National Council for Educational Research and Training. He has a Master’s degree in pure mathematics from the University of Calcutta with a uniformly brilliant academic career and Ph.D. in history of mathematics, and he finds interest in studying law, statistics, Sanskrit grammar, and Siddhanta Jyotisa (Indian astronomy). He is a recipient of the Nirodsasi Devi Gold Medal for work on ancient Indian astronomy and mathematics, and he has published a good number of research articles on the history of mathematics, presented papers in several international seminars on different topics of the history of mathematics, and delivered lectures on the subject at several universities. Siddheshwar Rameshwar Bhatt is Chairman of the Indian Philosophy Congress, Chairman of the Asian–African Philosophy Congress, and a national fellow of the Indian Council of Social Science Research, Government of India. With over 44 years of teaching experience, he has guided 44 Ph.D. and M.Phil. students. A recipient of 12 awards, Prof Bhatt, has authored 22 books on several topics in philosophy and social sciences.