Mathematics in India until 650 CE

Abstract

The chapter studies the mathematics of ancient India, from the Vedic (Indo-European) period, ca1500–500 bce, and later. They used a decimal system to express numbers, often of great size. The texts called Śulba-sūtras (Rules of the Cord, ca 800–200 bce) prescribe detailed rituals involving geometrical arrangements of bricks forming altars, using pegs and ropes. These texts present a system of mathematics involving the full application of the Pythagorean theorem, a rather precise approximation to the square root of 2, and approximate methods for squaring the circle and circling the square. Around 500 bce, the place-value decimal system was created, including the zero. Moreover, the bhūta-saṃkhyā system allowed place-value numbers to be represented using a sequence of fixed words, e.g., “eyes” always meant “two.” The analysis of possible metrical forms led to the development of simple combinatorics, including a form of what we would call Pascal’s triangle. Jain mathematics speculated about types of infinity. Mathematical astronomy, from ca 400 ce, included computation of mean and true planetary positions, and computation of lunar and solar eclipses. The chapter concludes with brief surveys of notable Indian mathematicians.