Brahmagupta
Native spelling: ब्रह्मगुप्त
598–668, Bhillamala (present-day Bhinmal, Rajasthan), India (exact place unknown)
Indian mathematician and astronomer at the Ujjain observatory who gave the first systematic rules for arithmetic with zero and negative numbers, a general method for solving quadratic equations, and formulas for the area and diagonals of a cyclic quadrilateral.
Brahmagupta was born in 598 CE in Bhillamala, capital of the Gurjaradesa region and a center of learning in what is now Rajasthan, India; he is sometimes called Bhillamalacarya, 'the teacher from Bhillamala'. He later moved to Ujjain, then India's leading center for astronomy and mathematics, where he headed the astronomical observatory and remained until his death around 668 CE.
His principal work, the Brahmasphutasiddhanta (The Correctly Established Doctrine of Brahma, 628 CE), is a treatise on astronomy written in verse that also contains, almost as an aside, some of the most consequential mathematics of the period. Brahmagupta was the first known author to treat zero not merely as a placeholder in positional notation but as a number subject to explicit arithmetic rules — addition, subtraction, multiplication and, with some difficulty, division — and he gave analogous rules for negative numbers, describing them in terms of debts and assets. He stated a general rule, equivalent to the quadratic formula, for solving quadratic equations with both positive and negative roots, and studied indeterminate equations of the type later misattributed to Pell in Europe. In geometry, Brahmagupta's formula gives the area of a cyclic quadrilateral from its four side lengths, generalizing Heron's formula for triangles, and Brahmagupta's theorem describes a property of cyclic quadrilaterals whose diagonals are perpendicular.
Brahmagupta wrote a second astronomical manual, the Khandakhadyaka (665 CE), aimed at practical calculation. His work reached the Islamic world through an 8th-century Arabic translation known as Sindhind, transmitting the Indian decimal place-value system and the concept of zero westward, and it decisively shaped the later Indian tradition through mathematicians such as Bhaskara II.
Workplaces: Astronomical observatory, Ujjain
India