Ancient India Mathematics: 7 Discoveries That Changed the World

This article examines seven mathematical discoveries originating in ancient and medieval India that fundamentally transformed global mathematics, science, and technology. The seven discoveries examined are: the conceptualisation and formalisation of zero as a number (Brahmagupta, 628 CE); the decimal place-value system that all modern mathematics depends on; the trigonometric functions sine and cosine (Aryabhata, 5th century CE); the precursor to calculus — the Kerala School's infinite series expansions (Madhava of Sangamagrama, 14th century CE) predating Newton and Leibniz by 250 years; algebraic methods for solving linear and quadratic equations; combinatorics and the mathematical study of prosody (Pingala, 3rd century BCE); and mathematical astronomy including heliocentric models and calculation of Earth's circumference. Primary sources, historical transmission routes, and the political history of attribution are examined.