Paper Details

Ancient Indian mathematics played important roles in the development of concepts and methods that are now incorporated into number theory and algebra, as well as in notation. This paper investigates the evolution of place value notation in decimal systems, the use of zero, negative numbers, indeterminate equations, quadratic equations and cyclic methods for solving Pell-type equations. It is based on historical and analytical approach with emphasis on the works of Aryabhata, Brahmagupta, Mahavira and Bhaskara II; and on the overall mathematical tradition in Sanskrit of which they worked. The study suggests that; besides the significance of the discoveries, the significance of Indian Mathematics also includes its algorithmic style: the rules were formulated as general procedures, exemplified by a few cases, and communicated in commentaries. These accomplishments reinforced the computational aspects of arithmetic, broadened the range of numbers, and developed advanced techniques for equations whose solutions are limited to integers. Indian numerical and algebraic knowledge also had an impact on Islamic mathematics and European mathematical development, through translation and subsequent scholarly exchange.

Indian mathematics, number theory, algebra, zero, Aryabhata, Brahmagupta and Bhaskara II.