The Mathematics of Ancient India | Research & Encyclopedia Articles

It is widely believed that aside from the achievements of the ancient Greeks, Babylonians, and Egyptians, there was little progress in the area of early mathematics. In fact, many leading historians in this field have echoed that sentiment by either minimizing or ignoring the contributions of other cultures. However, India and its mathematicians were extremely important in the development of mathematical thought during antiquity, despite the reluctance of some authorities to question their contributions.

The contribution of early Indian mathematicians to contemporary mathematics cannot be overstated. Certainly their greatest contribution is our system of numbers. Since nearly all theories, principles, and constructs in this discipline rely on the number system, its development has had a tremendous impact on the field of contemporary mathematics. The novel Indian numerals were subsequently adopted by the Arabs, which eventually became known to Europe as Arabic numerals.

In addition, there were other notable contributions in the field of mathematics from this culture. While it is somewhat controversial, early Indian theorists are among the many groups who are credited with the invention and application of zero. The Indians were the first to use zero as a placeholder. Among the other important achievements were the estimation of π and the length of the solar year, each to four decimal places.

Many important documents from the early period of Indian mathematics have not survived or have survived only in the form of translations. Because of this, there are questions regarding the relationship between Greek and Indian mathematics. Original references are quite scarce, so it is difficult to credit one group with specific ideas. There are still many unanswered questions about the relationship between early mathematics in India and Greece. This becomes problematic in later centuries as well because of the proliferation of original materials, so that it is difficult to distinguish between ideas of European or Indian origin.

The earliest known mathematics of the region arose in the Indus valley in present-day Pakistan. It was associated with the Harappan civilization, which consisted of a few cities and many smaller villages scattered throughout the valley. The civilization was established around 2,500 B.C. and survived at least 800 years. The inhabitants were literate and had adopted a uniform system of weights and measures. Analysis of their system revealed that it was surprisingly similar to the one currently used in the United States. The "Indus inch" was 1.32 in (3.35 cm), which could be strung together in units of 10 to make a 13.2-in (33.5-cm) "Indus foot." An artifact made of bronze has also been discovered with discreet marks every 0.367 in (0.932 cm). One hundred of these would make the distance 36.7, which is a fair approximation of a yard, meter, and a grown man's stride length. Archeological evidence suggests that these units of length were used accurately by the Harappan civilization in their construction.

Perhaps the most famous evidence of the mathematical prowess of the early Indian civilizations is contained in the Sulbasutras. The Sulbasutras are ancient religious texts that contained, among other things, detailed geometrical knowledge in the form of instructions for building altars. While these were practical guides that were intended as mathematical texts, they nevertheless show how adept these early civilizations were at math.

Around the third century B.C., when the Sulbasutras are believed to have been written, the Brahmi numerals were developed. After several modifications, these numerals evolved into the standard 1, 2, 3, 4, 5, 6, 7, 8, 9 still used in modern times. While the Brahmi numerals themselves did not have place values, the Indian numbering system eventually developed a place value system, which turned out to be extremely simple, yet very elegant. It should also be noted that the Indian number system is almost exclusively base-10, as opposed to the other systems that developed at that time that used other base systems, such as base 20 or base 60. While the origins of the Brahmi numerals are questioned, there is ample evidence that subsequent cultures modified this system for their own use.

The next major civilization to have a significant impact on the development of mathematics in India was the Gupta. The Gupta period marked the time when the Gupta dynasty ruled over much of India from the early fourth centuryA.D. to the late sixth century A.D. This period is thought of as the Classical Age of India, characterized by new ideas and prosperity. The Gupta numerals developed from the Brahmi numerals, and these became known over large areas as the Gupta expanded their empire by conquering new territory. However, the greatest influence of the Gupta civilization was not the numerals themselves, but the utilization of a place-value system with them.

A place-value system is one that uses numerals standing for different values depending on their position relative to the other numerals. Although the Babylonians are credited with developing the first place-value system in about the nineteenth century B.C., the Indian number system was unique in that it used base-10, making our own numbering system a direct descendent of it. A historical document indicates that this system has been used in India since before 594 B.C. It is not known whether this system was developed independently of other cultures, or if its inception was due to the influence of the Greeks, Babylonians, or possibly even the Chinese. However, we do know that this system was conveyed to other cultures, where it had a profound impact on the development of mathematics.

The religious and philosophical group called the Jains also shaped the mathematics of India. The Jains were founded in the sixth century B.C. They worked on problems such as number theory, cubic equations, quadratic equations, and statistics. They also had an understanding of advanced ideas such as that of infinity. Their work was later summarized and expanded by Aryabhata (476-550?), the most important ancient mathematician from that region.

Aryabhata headed the classical era of Indian mathematics. He helped to ignite a new era in mathematics, which in turn spurred on other sciences, such as astronomy. He recognized the importance of scientific investigation and established research centers to fulfill that goal. Among his many accomplishments were the introduction of the concept of trigonometry, the most precise estimation of π up to that date, and an accurate estimation of a solar year.

India's contributions to the development of mathematics played a vital role in establishing our system of numbers, and provided many other fundamental concepts as well. Throughout antiquity, no other cultures surpassed those of the Indian subcontinent when it came to the development and implementation of the science of mathematics.

The tremendous impact that Indian mathematicians had on the development of mathematical concepts is often obscured because of unsubstantiated evidence, inappropriate credit to other cultures, prejudice, and, finally, just plain ignorance. Evidence is mounting, however, that India was at the forefront of mathematical thought. It has been well established that our system of numbers has its roots firmly planted in India. Not only did we inherit the written appearance of our numerical characters from ancient India, we also borrowed their base-10 place-value system of numbers, which is still used today. Without this, mathematics as we know it would simply not exist. The ancient Indians provided a useful, flexible, and intuitive model for us to use.

It is hard to imagine what mathematics would be today without our current number system. Things we take for granted in every day life, such as money, are based on this system. The implementation of a place-value system is so elegant and practical that we often take it for granted. It is one of the most important mathematical developments in history.

Another important element that India contributed to the world of mathematics is the work of Aryabhata, who extolled the virtues of scientific research. This spurred on further scientific study, which served as a model for future generations of scientists. By establishing research centers, Aryabhata provided the impetus and desire to further knowledge in the field. As the knowledge of mathematics grew, so did the knowledge of physical sciences by its application. As an example, great advances were made in geography and astronomy as a direct result of having the mathematics necessary to solve problems.

Among the significant contributions made by individuals, Aryabhata himself provided the answers to many important questions and helped developed the branch of mathematics called trigonometry. He is often credited with the development of zero as a placeholder, although some historians credit one of his pupils with that achievement. This had tremendous implications for mathematics and made it much easier to signify certain numbers. Modern society certainly owes a huge debt to those ancient scientists and mathematicians.

Murthy, T. S. Bhanu. A Modern Introduction to Ancient Indian Mathematics. New Delhi: Wiley Eastern, 1992.

Neugebauer, Otto. The Exact Sciences in Antiquity. New York: Dover Publications, 1969.

Thibaut, G. Mathematics in the Making in Ancient India. Calcutta: K.P. Bagchi, 1985.

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