Bijaganita Of Bhaskaracarya.pdf

Pierre de Fermat's problem, posed in 1657, was to find all integers satisfying the equation Dx^2 + 1 = y^2, where D is a fixed positive integer that is not a perfect square. However, ancient Indian mathematician-astronomer Brahmagupta had investigated the same problem almost six centuries earlier and came up with a composition law, and subsequent Indian algebraists developed an algorithm called cakravāla to solve it. Bhāskarācārya's algebra text Bījagaṇita, written in 1150 CE, describes the bhāvanā law and the cakravāla algorithm in Sanskrit verses, and also discusses integer solutions to linear equations, negative numbers, zero, variables, and the fundamental operations with them. The text introduces infinity in mathematics, defining rules for interactions with usual numbers, and its verses are in the anuṣṭup metre, with touches of mythological allegories. Bhāskarācārya emphasizes the importance and power of algebra, venerating the Unmanifested and paying tribute to the wise mathematician who solves problems using algebra.