The main work of Brahmagupta, Brahmasphutasiddhanta (The Opening of the Universe), written in 628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both positive and negative numbers, a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series, Brahmagupta's Identity, and the Brahmagupta’s theorem. Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ... In mathematics, Brahmaguptas identity says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares. ... Brahmagupta’s theorem states that in a cyclic quadrilateral (a four-sided shape whose corners lie on a circle) having perpendicular diagonals, the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. ...
He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote two texts on mathematics and astronomy: the Brahmasphutasiddhanta in 628, and the Khandakhadyaka in 665.
The Brahmasphutasiddhanta is the earliest known text other than the Mayan number system to treat zero as a number in its own right.
It goes well beyond that, however, stating rules for arithmetic on negative numbers and zero which are quite close to the modern understanding.
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