Early Indian Mathematics

2.1 The Sulba Sutras

The earliest Indian mathematical texts are the Sulba Sutras (c. 800–500 BCE), appendices to the Vedas that contain rules for constructing sacrificial altars. These texts include geometric constructions equivalent to the Pythagorean theorem, methods for approximating square roots, and techniques for transforming one geometric shape into another of equal area.

The Baudhayana Sulba Sutra gives an approximation of √2 as 1 + 1/3 + 1/(3·4) − 1/(3·4·34) = 1.4142156..., which is accurate to five decimal places. This predates any comparable accuracy in the West by centuries.

2.2 Aryabhata and the Classical Period

Aryabhata (476–550 CE) wrote the Aryabhatiya at age 23, a compact treatise covering arithmetic, algebra, plane trigonometry, and spherical trigonometry. He computed π ≈ 3.1416 and developed one of the first sine tables.

Aryabhata proposed that the Earth rotates on its axis (a millennium before Copernicus made this argument in Europe) and gave a remarkably accurate value for the length of the sidereal year. His work had enormous influence on subsequent Indian astronomy and, through Arabic translations, on Islamic and later European science.

2.3 The Invention of Zero

India's most profound gift to mathematics is the decimal place-value system with zero as both a placeholder and a number in its own right. While Babylonians had a placeholder symbol and the Maya independently developed zero, the Indian system — fully positional, with zero as an operational number — became the universal standard.

Brahmagupta (598–668 CE) was the first to state explicit rules for arithmetic with zero and negative numbers. The Indian numeral system traveled to the Islamic world via trade and scholarly exchange, was adopted and refined by Arabic mathematicians, and eventually reached Europe through Fibonacci in 1202 — where it displaced the cumbersome Roman numeral system.

2.4 Key Contributions