The Decimal System and Zero
India gave the world the place-value decimal system and the treatment of zero as a number. Brahmagupta (around 628 CE) formalised the arithmetic rules for zero and negative numbers, ideas that reached Europe through Arabic scholarship and now underpin all modern computation.
Aryabhata
Aryabhata (476 CE), in the Aryabhatiya, gave an accurate approximation of pi, compiled sine tables, provided methods for areas and volumes, and proposed that the Earth rotates on its axis, a remarkable insight for his era.
Brahmagupta and Bhaskara
Brahmagupta advanced algebra and rules for solving quadratic equations, while Bhaskara II, in the Lilavati and Bijaganita, developed sophisticated algebra and early ideas resembling differential calculus.
The Kerala School and Madhava
Madhava of Sangamagrama and the Kerala School (14th to 16th centuries) derived infinite series for pi, sine and cosine, anticipating key results of calculus by roughly two centuries.
Modern Relevance
These contributions form the basis of number systems, numerical methods and algorithms used across computer science and engineering today.