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Introduction

Throughout the history of man's intellectual development and expansion of his understanding of the world around him, there has been a gradual unification of seemingly disjoint areas of knowledge: art and religion, biology and psychology, and so on. Mathematics and philosophy are two areas of knowledge that have also developed through such a symbiotic relationship; many historically renowned mathematicians, such as Rene Descartes, are also known for advancing their own philosophical ideas, such as Descarte's famous dictum, Cogito ergo sum.

However, on the whole, it is not terribly common for a concept or idea in one field to spawn another idea or concept in another field, especially in the case of mathematics and philosophy, since one field is the basis for virtually all of man's scientific advancements, while the other is a cornerstone for virtually all of man's spiritual development. This is not to say that there are no such occurrences in these two areas. In fact, one of the most important developments in the entire history of mathematics had its roots in the teachings of one of the most influential religions in the world today. The invention of the number zero and the subsequent development of a written representation for the number zero, which is considered by many scholars to be among the most influential and important developments in mathematics, had its beginnings in the philosophies of various religious figures in the Indian civilization over two thousand years ago.

It came from India...

Although the identity of the actual inventors of the number zero is highly contested by scholars of today, most scholars agree that the number zero and the circular symbol which represents this number originated in India approximately during the ninth century. However, there is good reason to believe that the concept of the number zero, if not the symbol for zero, was already in common usage among Indian mathematicians at least a century before, depending on sources consulted; in fact, there are some scholars who refer to a manuscript dating approximately from the second century B.C.E. that uses the number zero in the computation of the number of arrangements of two different items in an unknown number of places (Datta 75).

Regardless of the exact date of the origination of the zero, it can be said that until the Indian number system, along with their symbol for zero, was imported into Baghdad in the middle of the ninth century, Indian mathematicians stood alone in the world as they developed an increasing number of methods for various computations and applications using the number zero in one way or another. In fact, all known Hindu treatises on arithmetic and algebra contained a section entirely devoted to basic mathematical operations involving the number zero (Datta 80). Earlier manuscripts show the zero being used to represent placeholders in numbers such as one million, while later manuscripts show the zero considered as an actual number, like one and two, which one can manipulate and use in computations instead of using the zero as a mere placeholder. Some manuscripts of the eighth century even used the symbol for zero to represent unknown quantities in equations, much as mathematicians use x, y, and z to represent unknown quantities in equations today.

The religious connection...

But why India? Why is it that the Indus Valley civilization had a symbol and a concrete understanding of the concept of zero, and no other civilization up until the ninth century had a zero? To begin to traverse the path to answer this question, the etymology of the word "zero" must be examined. The word "zero", as well as its rather archaic synonym "cipher", both come from the Arabic sifr, which means "vacant"; this Arabic word, in turn, comes from the Sanskrit word sunya, which means "vacant" or "void" (Karpinski 152). Surely, the concept behind the word "nothing" predates even the Indus Valley civilization. However, even if previous civilizations understood that there existed such a concept as nothing, no civilization seemed to deem it important enough to actually consider the concept of nothing as an integral part of the reality in which they lived; otherwise, the Greek civilization, whose mathematical contributions such as the Pythagorean theorem and the numerous theorems from pre-collegiate geometry are well-known even by the occasional dabbler in mathematics, might have realized that their mathematical computations might have benefited by such a concept as the number zero.

The reason as to why the Indian civilization was the first civilization to develop widespread application of the concept of zero in mathematics and the sciences can be found in the religious aspect of the Indian civilization. Specifically, the concept of nothing and its importance can be found in the teachings of Mahayana Buddhism during the second century, and in Buddhism in general, whose presence in India was felt as early as the sixth century B.C.E. Classical Buddhism–that is, Buddhism derived mainly from the teachings of Siddartha Gautama–has as one of its central tenets the idea of sunyata, which literally means "emptiness". Sunyata is emptiness in the sense that every event in the universe is merely relative and not absolute, nor does any event possess any self-subsistence (Smart 95). Nagarjuna, arguably one of the most famous Indian Mahayana Buddhist philosophers, took the idea of sunyata a step farther and taught in his philosophical writings, written during the second century, that all things are "empty" in that nothing has its own nature in itself (Smart 110). Nagarjuna also extended this "philosophy of emptiness" further than "classical" Buddhism in naming the otherwise indescribable Ultimate or Truth beyond the Reality which is perceived by those who have not yet attained nirvana as the Sunya, which is the Sanskrit word for void. It can be seen, therefore, that the Indian civilization was the only major civilization at the time to have the idea of "nothing" incorporated into its own spiritual or religious aspect; thus, it would make sense that the Indian civilization would be the first civilization to develop fully the concept of zero and to apply this concept towards the advancement of mathematics, the sciences, and the expansion of scientific knowledge in general.

Usage of the zero...

Another interesting reason why the Indus Valley civilization should be the logical choice for the origin of the zero, in retrospect, is the fact that no other civilization at the time made use of the gigantic numbers that the Indian civilization did. Even though most religions at this time, as well as the religions of past civilizations, were polytheistic, none had as many divine and semi-divine entities as the Hindu faith. Traditionally, there are 330 million gods that are reverenced by Hindus throughout India (Smart 40). Also, in many works of Hindu, Jain, and Buddhist literature, numbers much greater than one million are commonplace. For example, in the Ramayana, a spy narrates to his sovereign king the exact number of troops that are in his rival's army; the number of men in the army would be represented, if written out, as the number one, followed by sixty-two zeroes (Srinivasiengar 3). Obviously, without the number zero, this type of numerical quantity would have been impossible to write. As a final example of how the Hindus used the zero prodigiously in their own religion, it is interesting to note that Hindus of today believe that the human race is living in the age of the Kali Yuga, one of four epochs through which the world is to exist before being destroyed to become renewed. The length in years of the Kali Yuga is 432,000 years, and the three ages that preceded the present Kali Yuga were even longer in duration (Srinivasiengar 4).

The physical shape and appearance of the number zero as a circle also gave rise to rather frequent uses of the number zero in poetry. Besides the many mathematical treatises which often contained problems posed as sections of verse, there were plenty of non-mathematical poems containing the number zero. The following is an excerpt from the Vâsavadattâ, written by the Indian poet Subandhu:

And at the time of the rising of the moon with its blackness of night, bowing low, as it were, with folded hands under the guise of closing blue lotuses, immediately the stars shone forth, like zero-dots (sunya-bindu), because of the nullity of metempsychosis, scattered in the sky as if on the ink-blue rug of the Creator who reckoneth the sum total with a bit of the moon for chalk. (Datta 81)

The term sunya-bindu, or "zero-dots", in the passage refers to the written symbol for zero. Usually, the zero would be written as a circle, but almost as often, the zero would be represented by a mere dot, a physical metaphor for the concept which the symbol represented to the reader.

All of this for nothing?!?

It is rather ironic, in a somewhat humorous manner, that so much has been made of the development of a concept signifying and giving an actual mathematical name to the idea of nothing; the expression "making a big deal out of nothing" may come to mind. However, it also seems rather unbelievable that even if the idea of nothing is rather basic to man's perception of reality, especially that part of reality which can be viewed as a mathematical abstraction–illustrated by the simple abstract concept of addition and subtraction of objects–the idea of representing nothing by a mathematical symbol came to someone's mind relatively late in the time-scale of man's intellectual history. As Macbeth may have said, the historical reaction to the development and usage of the number zero may be likened to a storm, "full of sound and fury, signifying nothing."


Bibliography

Datta, Bibhutibhusan and Singh, Avadesh Narayan, History of Hindu Mathematics: A Source Book. Bombay, Asia Publishing House, 1962.

Karpinski, Louis Charles, The History of Arithmetic. New York, Russell & Russell, Inc., 1965.

Sanford, Vera, A Short History of Mathematics. Cambridge, Massachusetts, Houghton Mifflin Company, 1958.

Smart, Ninian, Religions of Asia. Englewood Cliffs, New Jersey, Prentice Hall, Inc., 1993.

Srinivasiengar, C.N., The History of Ancient Indian Mathematics. Calcutta, The World Press Private Limited, 1967.

Younger, Paul, Introduction to Indian Religious Thought. Philadelphia, Pennsylvania, The Westminster Press, 1972.