History of Hindu Mathematics: Book 1, Chapter I, Section 1: A Glimpse of Ancient India

Chapter I

Numeral Notation

1. A Glimpse of Ancient India

The student of ancient Indian History is struck by the marvellous attainments of the Hindus, both in the Arts and the Sciences, at a very early period. The discoveries at Mohenjo-daro reveal that as early as 3,000 B.C. the inhabitants of the land of the Sindhu—the Hindus—built brick houses, planned cities, used metals such as gold, silver, copper and bronze, and lived a highly organised life. In fact, they were far in advance of any other people of that period. The earliest works available, the Vedas (c. 3,000 B.C. or probably much earlier), although consisting mainly of hymns of praise and poems of worship, show a high state of civilisation. The Brâhmaṇa literature (c. 2,000 B.C.) which follows the Vedas, is partly ritualistic and partly philosophical. In these works are to be found well-developed systems of metaphysical, social and religious philosophy, as well as the germs of most of the sciences and arts which have helped to make up the modern civilisation. It is here that we find the beginnings of the science of mathematics (arithmetic, geometry, algebra, etc.) and astronomy. This period was followed by more than two thousand years of continuous progress and brilliant achievements. Although during this period there were several foreign invasions as well as internal wars and many great kingdoms rose and fell, yet the continuity of intellectual progress was maintained. The constitution Page 2 of Hindu society was mainly responsible for this. The foreign invaders, instead of being a hindrance, contributed to progress and the strengthening of Hindu society by bringing in new blood. They settled in the land, adopted the religion and customs of the conquered and were completely absorbed into Hindu society. There were a class of people—the Brâhmaṇas—who took the vow of poverty, and devoted themselves, from one generation to another, to the cultivation of the sciences and arts, religion and philosophy. The Brâhmaṇas, thanks to their selflessness and intellectual attainments, were highly respected by the kings and the people alike. They were the law-givers and advisers of the kings. In fact, this body of selfless thinkers and learned men were the real rulers of the land.

The great Epic, the Râmâyaṇa, was composed by Vâlmîki, the father of Sanskrit poetry, about 1,000 B.C., Pâṇini, the grammarian, perfected Sanskrit grammar about 700 B.C. and Suśruta wrote on the sciences of medicine and surgery about 600 B.C.¹ A century later, Mahâvîra and Buddha taught their unique systems of religious and moral philosophy, and the doctrine of Nirvâṇa. With the spread of these religions evolved the Jaina and Buddhist literatures. Some of the earlier Purâṇas and Dharma-śâstras were written about this time. The period 400 B.C. to 400 A.D., however, seems to have been a period of great activity and progress. During this period flourished the great Jaina metaphysician Umâsvâti, Patañjali, the grammarian and philosopher, Kauṭilya, the celebrated politician, Nâgâjuna, the chemist, Caraka, the physician, and the immortal poets Aśvaghoṣa, Bhâsa and Kâlidâsa. The great Page 3 astronomical Siddhântas, the Sûrya, the Pitâmaha, the Vaśiṣṭha, the Parâśara and others were written during this period and the decimal place-value notation was perfected.