Brahmagupta Formalises Zero
Brahmagupta wrote down the rules for calculating with zero and with negative numbers in 628. He was the head of the observatory at Ujjain, then the leading centre of Indian astronomy, and the Brahmasphutasiddhanta is an astronomical work with two chapters of pure mathematics in it. Zero as a placeholder was older — the Babylonians used a gap and then a sign, and Indian scribes had a dot — and what Brahmagupta supplied was zero as a number to be operated on. His rules are stated in verse and in commercial language, with positive quantities called fortunes and negative ones debts: a debt subtracted from nothing is a fortune, the product of two debts is a fortune, the sum of a fortune and an equal debt is zero. That is the first written statement anywhere of the arithmetic of negative numbers, which European mathematicians were still refusing to accept as legitimate a thousand years later. He got division by zero wrong, which is the standard footnote; he says a positive or negative number divided by zero is a fraction with zero as denominator, and elsewhere that zero divided by zero is zero. He also gave a formula for the area of a cyclic quadrilateral, solutions to indeterminate equations, and an accurate interpolation method. The work reached Baghdad in the eighth century, was translated into Arabic, and travelled from there into Latin — which is why the digits are called Arabic and the system is Indian. The transmission is worth stating plainly. Al-Khwarizmi wrote the Arabic account in the ninth century, Fibonacci brought it to Italy in 1202, and Europe took another three centuries to adopt it because merchants' guilds and city governments repeatedly banned the new numerals as too easy to forge.
- Year: 628 CE
- Category: Cultural
