Aryabhatiya, written by Aryabhata in the 5th century CE, is a seminal work in Indian mathematics that includes important contributions to algebra, including the use of variables, the concept of zero, and the development of algebraic equations.

Pingala, an ancient Indian mathematician and prosodist, is credited with discovering the Fibonacci sequence and the golden ratio in the 2nd century BCE. He used these concepts in his work on Sanskrit prosody and meter.

Modular arithmetic, a concept developed by Indian mathematicians, is widely used in computer science for various applications, including cryptography, data compression, and error correction.

Indian mathematics played a crucial role in the development of the Indian calendar system by providing accurate astronomical calculations, developing algorithms for timekeeping, and creating mathematical models for planetary motion.

Linear programming, a technique developed by Indian mathematicians, is widely used in operations research to solve optimization problems with linear objective functions and constraints.

Indian mathematics made significant contributions to ancient Indian architecture by providing geometric principles for constructing temples and monuments, developing mathematical formulas for structural stability, and creating mathematical models for acoustics and lighting.

Wavelet transform, a mathematical technique developed by Indian mathematicians, is widely used in signal processing and image compression for analyzing and representing signals and images efficiently.

Indian mathematics played a crucial role in the development of ancient Indian astronomy by providing accurate methods for calculating planetary positions, developing mathematical models for predicting eclipses, and creating mathematical tables for astronomical observations.

Public-key cryptography, a concept developed by Indian mathematicians, is widely used in cryptography to secure data and communications by using a pair of keys, a public key, and a private key.

Indian mathematics made significant contributions to ancient Indian medicine by providing mathematical models for understanding the human body, developing mathematical formulas for calculating drug dosages, and creating mathematical tables for medical diagnosis.

Stochastic processes, a concept developed by Indian mathematicians, are widely used in finance and economics to model financial markets and investment strategies by taking into account random fluctuations and uncertainties.

Indian mathematics played a crucial role in the development of ancient Indian metallurgy by providing mathematical formulas for alloy compositions, developing mathematical models for heat treatment processes, and creating mathematical tables for metal properties.

Fractal geometry, a concept developed by Indian mathematicians, is widely used in computer graphics and animation to create realistic and visually appealing images by simulating natural patterns and textures.

Indian mathematics made significant contributions to ancient Indian music by providing mathematical formulas for musical scales and intervals, developing mathematical models for musical harmony and rhythm, and creating mathematical tables for musical instruments.

Neural networks, a concept developed by Indian mathematicians, are widely used in artificial intelligence and machine learning to develop intelligent systems and algorithms that can learn from data and make predictions.