Brahmagupta Formalises Zero
A century after Aryabhata's Aryabhatiya introduced positional decimal notation at the Gupta court, the mathematician Brahmagupta, working at the same astronomical centre of Ujjain, took the decisive further step: in his Brahmasphutasiddhanta (628 CE), he laid out explicit rules for arithmetic operations involving zero, treating it for the first time as a number with defined mathematical properties rather than merely a placeholder symbol -- rules for adding, subtracting, and multiplying by zero, and (with less success, since he could not resolve the resulting contradictions) an attempt to define division by zero. Brahmagupta's work also gave systematic treatment to negative numbers, which he called 'debts' as opposed to 'fortunes' (positive numbers), and provided solutions to quadratic equations and to what is now called Pell's equation centuries before European mathematicians addressed the same problems. This Indian positional decimal system, with zero as a genuine number, spread west along established trade and scholarly networks: the 9th-century Baghdad mathematician Al-Khwarizmi (whose name gave us 'algorithm') transmitted and extended Indian arithmetic in his own treatises, and the system reached Latin Europe in the 12th-13th centuries, arriving via Arabic intermediaries and consequently known in the West as 'Arabic numerals' -- obscuring their Indian origin, though the numerals themselves are still called Hindu-Arabic numerals in more careful scholarly usage.
- Year: 628 CE
- Category: Cultural
