Brahmagupta

Brahmagupta gave the first systematic rules for arithmetic with zero and negative numbers. Born in 598, probably at Bhillamala in what is now Rajasthan, he directed the astronomical observatory at Ujjain, the leading centre of Indian mathematics and astronomy. He wrote the Brahmasphutasiddhanta in 628, at thirty, and the Khandakhadyaka thirty-seven years later. Chapter eighteen of the first contains the arithmetic. Zero had been used as a placeholder before him; Brahmagupta treated it as a number and defined operations on it — that a number minus itself is zero, that a number added to or subtracted from zero is unchanged, and that zero multiplied by anything is zero. He got division by zero wrong, giving zero over zero as zero, which nobody resolved for a thousand years. He also gave rules for negative numbers, which he called debts against fortunes: a debt minus zero is a debt, the product of two debts is a fortune, and the square root of a fortune has two values. He solved linear and quadratic equations, gave a general solution to certain indeterminate equations later called Pell's equation, and produced a formula for the area of a cyclic quadrilateral that generalises Heron's for triangles. His astronomy calculated eclipses, planetary positions and the length of the year, and he attacked the notion that eclipses are caused by demons. He also insisted, against his own tradition, that the earth is a sphere. The work reached Baghdad in the eighth century and was translated into Arabic, which is how the decimal system and zero travelled west. He died around 668.

• Lived: 598 CE – 668 CE
• Nationality: Indian
• Roles: mathematician, astronomer