Indian mathematics

Indian mathematics comprises mathematical traditions developed in the Indian subcontinent, from ancient geometry and astronomy to advances in algebra, arithmetic, and calculus.

Hindu–Arabic numeral system: The decimal positional numeral system using the digits 0 through 9, transmitted from India through the Islamic world to Europe. Its Indian forms made positional arithmetic compact and practical.
Aryabhata's algorithm for square roots: A procedure described by Aryabhata for extracting square roots of numbers expressed in decimal notation. It exemplifies the tradition’s systematic methods for numerical calculation.
Sulba Sutras: Ancient Sanskrit texts containing geometric rules for constructing Vedic fire altars. Their construction problems preserve some of the earliest known Indian mathematical techniques.
Aryabhata: An Indian mathematician and astronomer who composed the Aryabhatiya in 499 CE. His treatise presents influential arithmetic, algebraic, and trigonometric results.
Transmission of the Hindu–Arabic numeral system: The historical movement of Indian decimal numerals through Arabic scholarship into Europe and other regions. This transmission carried Indian place-value arithmetic into global use.
Zero: A number representing no quantity that also functions as a placeholder in positional notation. Indian mathematicians developed zero into both a numeral and an arithmetic object.
Kuttaka: An iterative Indian algorithm for solving certain linear indeterminate equations in integers. This method turns a difficult class of equations into a sequence of arithmetic reductions.
Śulbasūtra geometry: Geometric knowledge in the Śulbasūtras, including rules for altar dimensions and diagonal lengths. It shows geometry emerging from precise ritual construction.
Brahmagupta: An Indian mathematician and astronomer who wrote the Brahmasphutasiddhanta in 628 CE. He stated systematic rules for arithmetic with zero and negative numbers.
Al-Khwarizmi: A ninth-century Persian scholar whose works helped introduce Indian numerals and algebraic methods to Arabic readers. His account of Indian calculation helped transmit the numeral system westward.

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