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Familiar too are many of the arithmetic and algebraic techniques involving Indian numerals. Some historians of mathematics have deplored these aspects of the Indian tradition, seeing in them merely a habit of rote memorization and an inability to distinguish between true and false results.

This article covers the history of mathematics in the Indian subcontinent from ancient times through the beginning of the colonization of the region by Great Britain. During and after the 19th century, Indian mathematics merged with the modern Western stream of mathematics. Thus, for later mathematical developments in this region, see mathematics: Mathematics in the 19th and 20th centuries. Sanskrit, the classical language of India and the chief medium for its premodern mathematical texts, maintained a strictly oral literary tradition for many centuries.

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Even after writing was introduced, the traditional writing materials, such as palm leaves, birch bark, and later paper, did not last long in the South Asian climate. The earliest surviving Sanskrit references to mathematical subjects are some number words in the Vedas , ancient sacred texts that were passed down by recitation and memorization.

The oldest surviving Veda manuscript dates from the 16th century. Although the Indian number system seems always to have been decimal, in the Satapatha Brahmana c. This is reminiscent of the structure of ancient Babylonian sexagesimal division tables and may indicate as do some later astronomical texts the influence of the base mathematics of Mesopotamia. The people who left these traces of their thinking about numbers were members of the Brahman class, priestly functionaries employed in the preparation and celebration of the various ritual sacrifices.

Using simple tools of ropes and stakes, the altar builders could produce quite sophisticated geometric constructions, such as transforming one plane figure into a different one of equal area.

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The recorded rules also indicate knowledge of geometric fundamentals such as the Pythagorean theorem , values for the ratio of the circumference of a circle to its diameter i. Different shapes and sizes of sacrificial altars were described as conferring different benefits—such as wealth, sons, and attainment of heaven—upon the sponsor of the sacrifice. Perhaps these ritual associations originally inspired the development of this geometric knowledge, or perhaps it was the other way around: the beauty and harmony of the geometric discoveries were sacralized by integrating them into ritual.

During the rise of Buddhism and Jainism after bce , the connection between mathematical and religious thought persisted. But instead of altar constructions for animal sacrifices, which Buddhist and Jain principles rejected, mathematics supplied a framework for cosmological and philosophical schemes.

Jain authors in particular employed immense numbers even infinity in elaborate and vast models of the universe. These new religions, as well as the older Vedic religion—by this time mostly shorn of ritual animal slaughter and more akin to modern Hinduism —also required mathematical techniques for astronomical models in order to maintain their calendars. Other applications of mathematics, such as in commerce and administration, must also have flourished at this time, although only occasional brief allusions survive.

For instance, a Buddhist text c. London: Elsevier. Rajagopal, C.

Ancient traces

Ramasubramanian, K, and M. Tantrasangraha of Nilakantha Somayaji. Guildford, Surrey: Springer London. Sarma, K. Hoshiarpur: Vishveshvaranand Institute. Hoshiarpur: Vishveshvaranand Vedic Research Institute.

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Ramasubramanian, M. Srinivas, and M. Ganita-Yukti-Bhasa of Jyesthadeva. Sastri, Sambasiva, ed. The Aryabhatiya of Aryabhatacarya, with the Bhasya of Nilakanthasomatsutvan. Trivandrum: Government Press. Srinivas, M. Emch, R.

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    Gupta, R. Plofker, Kim. Mathematics in India.