Brahmagupta (c. 588 or c. 598 A.D. - c. 600 or 665 A.D.; India)

Brahmagupta was a mathematician but he is also noted as being the last and most accomplished of all of the ancient Indian astronomers. In 628 A.D., Brahmagupta was the first person to use the mathematical concept of negative numbers to represent debts and positive numbers to represent assets as developed by the Hindus. It was Brahmagupta who developed the rules for the four operations ( addition, subtraction, multiplication and division) using negative numbers. Brahmagupta did not however present any definitions, axioms or theorems.

Brahmagupta's two chief works were entitled, Khandakhadyaka and the Brahmasiddhanta. The Brahmasiddhanta, written in 628 A.D., opposed some of the Hindu findings on astronomy which had been established on a scientific basis in 476 A.D. It consisted of twenty-five chapters, twenty-three of which dealt with astronomy- most specifically lunar and solar eclipses, planetary conjunctions, lunar phases and the determination of the positions of the planet. The remaining two chapters dealt solely with mathematical concepts such as arithmetic progression, quadratic equations and the proving of geometrical theorems associated with surface and volume. In the Khandakhadyaka, Brahmagupta simply tried to simplify the already existing system. In the field of mathematics, Brahmagupta is most noted for his cyclic quadrilateral equation (Britannica, 2:461, 1994; Encyclopedia Americana, 4:410, 18:496, 24:614, 1991: and Barba, p. 64, 1995).