Brahmagupta was the head of astronomical observation at Ujjain in Northern India. During the 7th century this was the most important centre of mathematical learning in India. We have two of his books the Khandakhadyaka written later in his life and the extraordinary Brahmasphutasiddhanta written in around 628.
This book discusses astronomy, but for the first time it looks at how we can study astronomy using algebra. It helped to define how Indian mathematics developed, with its focus on algebra and arithmetic. It also greatly influenced later Islamic mathematicians.
The book is interesting for a number of reasons. Brahmagupta when he does multiplication uses the place value of numbers almost as we would today. He also looked at positive and negative numbers and defined zero as the result of subtracting a number from itself. While some of his assumptions proved wrong - zero divided by zero is not zero - the work was a brilliant attempt to extend arithmetic to zero and to negative numbers.
He also produced a valuable formula for computing sines and an algorithm for computing square roots. But he is best remembered for his elegant formula for calculating the area of a cyclic quadrilateral.