Indian Decimal Numeration

Timeline

1. 401–501Core region of the Gupta Empire in northern India · IndiaUnder the Gupta Empire, Indian mathematicians adopted decimal place-value notation: each digit was represented by a distinct symbol, place value determined by written position, and an empty place implying the existence of zero. This system was better suited to large-number arithmetic and astronomical calculation than additive systems like Roman numerals.
2. c. 499–550Kurukshetra · HaryanaThe mathematician Aryabhata used decimal notation in the Aryabhatiya for astronomical constants and arithmetic calculations, and gave approximations for squares, cubes, and trigonometric functions, showing that the place-value system could already support complex scientific computation.
3. c. 505–587Ujjain · Madhya PradeshThe astronomer Varahamihira continued and spread decimal notation in works such as the Pañcasiddhāntikā, integrating astronomical calculations from multiple calendar systems and making place-value arithmetic a standard tool of the Indian scholarly community.
4. 598Bhillamala · RajasthanBrahmagupta first systematically set out in the Brahmasphutasiddhanta the rules for addition, subtraction, multiplication, and division of zero as an independent number, and discussed negative numbers, marking the decimal place-value system's theoretical completion in arithmetic and laying the mathematical foundation for its later transmission to the Islamic world and Europe.