The Great Art
This chapter discusses the origins of the art of algebra, beginning with the possibility that it may have come from the Greeks or from the Hindus. However, the Brahmins of northern India had some idea of algebra long before the Arabians learned it, contributed to it and brought that art to Spain in the late eleventh century. The Brahmasphutasiddhanta, written by the Indian mathematician Brahmagupta in 628, not only advanced the mathematical role of zero but also introduced rules for manipulating negative and positive numbers, methods for computing square roots, and systematic methods of solving linear and limited types of quadratic equations. The chapter also considers the contriburions of Abu Jafar Muhammad ibn Musa al-Khwārizmī and suggests that negative numbers originated in China, where they had been used since the beginning of the first millennium.