The Indian Concept of Zero in Mathematics

Timeline

1. 628–700Bhillamala · GujaratIn the Brahmasphutasiddhanta, Brahmagupta for the first time systematically gave the rules for addition, subtraction, multiplication, and division involving zero, defining zero (śūnya) as a number subtracted from itself, and discussed the arithmetic relations between negative numbers and zero, laying the theoretical framework for the Indian concept of zero.
2. c. 800–1030Indian subcontinent · Indian subcontinentMathematicians such as Shridhara and Mahavira developed algebraic applications of zero and place-value notation; circular or dot-shaped zero symbols appeared widely in Sanskrit manuscripts, and the Kerala school of southern India and the northwestern school routinely used decimal numerals containing zero in astronomical table calculations.
3. 1031–1040Ujjain · Madhya PradeshIn the 1030s Indian mathematicians still compiled ephemerides and astrological calculations using place-value notation containing zero, with the rules of zero's arithmetic already internalized as everyday mathematical practice; at the same time, Arab scholars in Basra and Baghdad translated Indian astronomical and mathematical works, and the concept of zero spread westward along with the Indian numeral system.