THE IMPERISHABLE SEED: How Hindu Mathematics Changed the World and Why this History was Erased
Students of mathematics learn of “Pascal’s Triangle”, “Fibonacci Sequence”, “Rolle’s Theorem” and “Taylor Series.” But they do not learn that these concepts were expounded much earlier than their supposed discoveries in Europe by Indian mathematicians such as Pingala, Hemachandra, Bhaskara and Madhava. Many of the fields of mathematics today— from the decimal representation of numbers and simple arithmetic to algebra, trigonometry, and even calculus—were developed by Hindu mathematicians or owe their origins to their works.
In The Imperishable Seed, Bhaskar Kamble assembles compelling evidence to show how this knowledge was created and transmitted to the rest of the world. He discusses the contributions of ancient and medieval India not only to mathematics, but also to fields such as astronomy and linguistics and how these contributions continue to find applications even today in areas such as computer science.
Finally, he traces why and how the tradition of Hindu mathematics in India came to an end and why most people today do not know about its history.
ForewordAlthough modern India gained political independence more than seventy years ago, its image in the West emerged out of European racism and colonialism to serve the purposes and goals of British Raj. ‘Every man carries with him through life a mirror, as unique and impossible to get rid of as his shadow,’ said the poet W. H. Auden, and this is true of societies as well. India has been unable to shake off or overwrite this image and its narratives remain informed by colonialist categories that are negated by its own experienced history.
The British foisted the false notion that India never had a scientific tradition. In reality, India was the world’s leading nation in science until four hundred years ago. Indian technology flourished before the arrival of the British, and it is estimated that India’s share of world trade in 1800 was about 25 percent.
When the mechanization brought about by the Industrial Revolution gave their own textiles a cost advantage, the British made sure that India was deprived of the resources to build its own factories. frombeingamanufacturingpowerhouse, Indiabecamedeindustrialized. It was turned into a huge market for British products. British Raj made token investments in science and technology
Jobs simply disappeared. Outside of farming and village crafts, and sparsely staffed revenue and medical departments and schools, one could only find work in the army or police or as clerks working for urban enterprises. Even when the railway system was built by the British, the employees for a long time could only be British or Anglo- Indians.
More and more people became servants and cooks, if they could find anything. Indians became office seekers. Any government position, even if only of the attendant in an office, was considered supremely desirable. Nearing the end of their depredations of India, the British created national services. In 1920, India’s scientific services had a total of 213 scientists of whom 195 were British!
Dharampal in his The Beautiful Tree shows how India’s own education system, which was widespread, cut across ‘caste’ lines and, in some regions, resulted in near 100% literacy. In dismantling this education system and replacing it with one which produced clerks for its Empire, Britain made sure that the English-educated Indian elite were fed on their biased understanding of India. The literacy rate in India on the British watch declined to about 12%, and a near complete loss of memory of its previous condition ensued.
Unfortunately, the colonial account is the foundation on which the intellectual life of the modern Indian elite rests. Repeated countless times, it forms the basis of instruction in schools and colleges, public policy, and the practice of law. People have internalized it and sincerely believe it to be the truth.
In 1837, Emerson delivered a famous speech, which in the words of Oliver Wendell Holmes became America’s ‘Intellectual Declaration of Independence.’ This speech pointed the direction America needed to take to actualize its destiny. India needs a similar intellectual independence to connect back to its genius,
Dr. Kamble’s The Imperishable Seed: How Hindu Mathematics Changed the World and Why It Was Erased From History is the announcement of this independence in the field of mathematics, the queen of the sciences. Rather than viewing Indian contributions as a footnote to the Western mathematical tradition as is generally done in history books, it shows that the facts are the other way around. Hindu mathematics changed the world in fundamental ways by providing some of the most revolutionary ideas on which contemporary mathematics and science is based.
Dr. Kamble’s book is based on impeccable research that is well known to scholars around the world, but due to Eurocentrism and academic inertia has not been woven into college or school curricula.
The book is an excellent read and timely for shaking people out of the cocoons of incorrect colonialist narratives. It will also be a great resource for those who wish to investigate the topics further.
Sometime in 2016 I was attending a German language class in Berlin, and the discussion happened to center around numbers. The teacher kept referring to the numbers we use today as ‘Arabic numbers’ to distinguish them from Roman numbers. When I pointed out to him that these are actually Indian numbers, he was surprised. I in my turn was surprised that he was surprised, since it reflected a general ignorance about a basic fact even among well-educated people in the West. Later I was to learn that my German teacher was no exception—the belief that ‘Arabic numbers’ come from Arabia is common among most Europeans. A similar incident, this time in an academic setting, occurred a few years later when I was attending a one-semester course on the history of mathematics at a university in Berlin. Considerable time was spent on Babylonian and Egyptian mathematics in the first few weeks, while the rest of the course was devoted to the mathematics of Greece and Europe. The professor vaguely mentioned about ‘Indian mathematicians’ once in the introductory lecture, and that was that. Once again I noticed how prominent India was by its absence—it was as if the Hindu civilization and its mathematics never existed. The omission was surprising, since the course specifically dealt with the history of mathematics.
Strange though it may sound, the situation is no better among Indians themselves, although most Indians are at least vaguely aware that numbers and the concept of zero come from India. However, that is where the knowledge stops, and most Indians remain woefully ignorant about the Hindu civilization’s rich mathematical heritage. The situation was not much different with me, and it was only in 2012 that I seriously started reading about the history of mathematics in India. I was astounded at how ignorant I had been all this time, and I was equally astounded at the prevalent notion that all mathematics comes from Greece and Europe. I was to learn that even calculus— that most prized possession of European mathematics—first made it appearance in Kerala four centuries before its appearance in Europe. But what really turned all my notions upside-down was when I read Prof. C. K. Raju’s thoroughly researched articles on how knowledge of the calculus was transmitted to Europe via Jesuit missionaries stationed in Kerala. It was clear that something major was amiss in how the history of mathematics is understood and presented today.
Based on all the reading I had done, sometime in early 2014 I wrote a series of articles on my blog on the history of Hindu mathematics. The idea of expanding the information so collected started taking shape in late 2015. Since there were already some excellent books on the history of Hindu mathematics, it was important for me to offer something new that was missing in these books. One immediate problem I noticed was that most of these books made no reference to the philosophy and knowledge structure of the Hindu civilization—the very same aspects that made the development of mathematics possible in the first place. In most books on the history of mathematics, Indian Mathematics, if it is discussed at all, is considered as a phenomenon independent from the knowledge structure from which it arose, and is exclusively discussed in terms of Western terminology and a Western framework. This is also common to many books that deal with Indian mathematics specifically. The problems with this approach are clear. It implicitly delegitimizes the Hindu framework of knowledge while legitimizing the Western framework, and fail to acknowledge, or even realize, how rooted the mathematics is in the philosophical foundations of the Hindu traditions.
Yet another problem I noticed was that a lot of interesting information on Hindu mathematics is scattered in different sources, books, and research articles. Also, the material is often technical, and all these reasons make it difficult for a layperson to easily access this information and to get a comprehensive overview of the subject.
My aim was thus to write a book that provides an overview of all major facets of Hindu mathematics, and which exhibits the close interplay between this mathematics and the deeper knowledge system from which it arose. I wanted to make the book as easy to unerstand as possible, and hence have put the more technical discussions into the appendices, which interested readers can follow up. I expect the book to be especially useful for high school students as they will see that most of the mathematics they learn in school comes from the Hindu civilization. It will also be useful to those who seek to know beyond the usual narrative of the Greek and European origins of mathematics. The book dicusses at length on Hindu philosophical ideas and knowledge systems to emphasize the connections of these systems with the mathematics that arose. Several verses from the original Sanskrit stating mathematical results are given. There is also a separate chapter on astronomy, as mathematics and astronomy were closely connected in the Hindu civilization, and some of the most beautiful applications of Hindu mathematics are to be found in astronomy. Just like mathematics, Hindu astronomy was in its time among the most advanced in the world, and this was certainly true till at least the 17th century.
The impact of Hindu mathematics and astronomy on the rest of the world has been immense, and I have discussed in considerable detail the transmission of mathematics and astronomy from India to the Arab world and to Europe, and its subsequent adoption in the rest of the world. It is a matter of wonder that in spite of having such far- reaching consequences, the mathematical achievements of the Hindu civilization remain largely unacknowledged in mainstream historical narratives. During the process of writing this book, I became intrigued with the question—why does this ignorance of Hindu mathematics exist in the first place? Closely related to this is the question—what were the reasons that made this thriving tradition of knowledge, arguably the most advanced in its time, suddenly come to a stop? Why are hardly any traces of it visible today? I have attempted to answer these questions in the final part of the book, where I have also given an account of the education system that was prevalent in ancient and medieval India.
The first version of the manuscript was completed in October 2019 which I submitted to Garuda publications. I am grateful to Dr.
D. K. Hari and Dr. D. K. Hema Hari for connecting me with Garuda, and for their unstinting support and interest in the project right from the start and for writing the foreword to the initial version of the book. The next several months were spent in a detailed editorial process with Sankrant Sanu. I am thankful to Prof. Ramasubramanian, IIT Mumbai, for interactions and help with translations of some of the Sanskrit texts, and to Prof. Subhash Kak, Oklahoma State University, for writing the foreword and for his valuable feedback.
Writing this book has been a very enriching experience. It was also a very painful experience at times, for it put me in touch with my own ignorance in particular and with the ignorance of Indian society in general regarding the heritage of the Indian civilization. It also showed me the tremendous amount of knowledge that was lost due to cultural and physical invasions across the centuries on the Hindu civilization. But more than that, it is the neglect on the part of the so-called educated Indians themselves in modern times that is the most painful. It is unfortunately all too true that after nearly 75 years of political independence, Indians are still taught to scoff at their own heritage in school right from a young age. They are still taught to look at their own civilization and history through the eyes of their former colonizers. The loss produced by this attitude and the resulting collective amnesia is perhaps the most insiduous as it accumulates over generations. This book is a humble attempt on my part to reverse this trend.
I would not have been able to complete this book had it not been for the love and support of my friends and family members. My wife Nia kept pushing me on to complete the book and her faith and support helped me to overcome the doubts which assailed me on frequent occasions. To Nia I am also indebted for several rounds of proof reading and for several helpful suggestions regarding the book’s structure, content and formatting. To my sister-in-law Yumi I am grateful for a through round of proof reading and for designing the cover for the earlier version of the book.
The long and interesting discussions I had with Sankrant Sanu, founder of Garuda publications, during the editing process of the book, coupled with Sankrant’s profound knowledge, wisdom and experience were instrumental in catapulting the standard of the book to a whole new level. His suggestions helped a lot in improving the overall structure of the book and several new topics were added based on his input.
The knowledge of Hindu mathematics and its impact on the world would have remained all but unknown had it not been for the work of countless scholars who tirelessly worked to preserve this knowledge. The works of these scholars have been invaluable in the writing this book, and here I take the opportunity of expressing my indebtedness to them all.
The tradition of mathematics in the Hindu civilization is extremely long and the literature available on this subject is correspondingly vast. It would be difficult indeed to do full justice to all aspects of Hindu mathematics in a single book, and hence it is inevitable that certain topics had to be omitted. Nevertheless, I do hope that it serves as a useful and interesting introduction to the legacy of mathematics in the Hindu civilization
In Chapter 11, I describe the close interactions between ancient India and ancient Greece. I also look at the philosophy of ancient India and ancient Greece more closely and explore strong signs of influence of Hindu philosophy on the philosophy of Socrates, Plato and other major Greek philosophers.
In Chapter 12, I discuss the transmission of Hindu mathematics to the rest of the world and its subsequent impact. This chapter is divided into two parts. The first part describes the transmission of Hindu mathematics to the Arabic world and subsequently to Europe. It highlights how several mathematical ideas ascribed to the Arabs are in fact Hindu inventions. The second part presents the overwhelming evidence and the series of ‘coincidences’ that show how calculus, whose discovery is popularly attributed to Newton and Leibniz, was transmitted from India to Europe via Jesuit missionaries stationed in Kerala.
In Chapters 13 and 14, I discuss respectively the reasons why the tradition of mathematics and other fields of knowledge declined in India, and why a general ignorance exists in today’s world regarding the contributions of the Hindu civilization and why this history has largely been omitted from the mainstream understanding of the history of science and mathematics even today.
Chapter 15 ends with a brief conclusion.