Photo: Pṛthūdhaka and Brahmagaputa · Public domain
Science · 628 CE

Brahmagupta’s Brahmasphutasiddhanta

Found
Written at Bhillamala (Bhinmal, Rajasthan) in the reign of the Chapa king Vyaghramukha
Kept at
Manuscripts in Indian libraries; printed editions

The astronomical work in which Brahmagupta, aged thirty, first set down rules for calculating with zero and negative numbers.

What it says

In the chapter on algebra Brahmagupta treats positive numbers as dhana, wealth, and negative numbers as rina, debt. He gives the rules: a debt minus zero is a debt, wealth minus zero is wealth, zero minus zero is zero; the product of two debts is wealth. He also solves quadratic equations and gives a formula for the area of a cyclic quadrilateral.

What it proves

It made zero a number in its own right. Translated into Arabic at Baghdad in the 8th century, it carried Indian mathematics west.

Evidence for