# List of Indian inventions and discoveries

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India is known for making some important contributions to science and technology which have helped shape the modern world. An abridged list is given below.

## Mathematics

• 800 BC: Indian mathematician Baudhayana, in his Baudhayana Sulba Sutra, discovers Pythagorean triples algebraically, finds geometric solutions of linear equations and quadratic equations of the forms ax2 = c and ax2 + bx = c, and finds two sets of positive integral solutions to a set of simultaneous Diophantine equations.
• 600 BC: Indian mathematician Apastamba, in his Apastamba Sulba Sutra, solves the general linear equation and uses simultaneous Diophantine equations with up to five unknowns.
• 100 BC: The Bakhshali Manuscript written in ancient India uses a form of algebraic notation using letters of the alphabet and other signs, and contains cubic and quartic equations, algebraic solutions of linear equations with up to five unknowns, the general algebraic formula for the quadratic equation, and solutions of indeterminate quadratic equations and simultaneous equations.
• Circa 499: Indian mathematician Aryabhata, in his treatise Aryabhatiya, obtains whole-number solutions to linear equations by a method equivalent to the modern one, describes the general integral solution of the indeterminate linear equation and gives integral solutions of simultaneous indeterminate linear equations.
• Circa 628: Indian mathematician Brahmagupta, in his treatise Brahma Sputa Siddhanta, invents the chakravala method of solving indeterminate quadratic equations, including Pell's equation, and gives rules for solving linear and quadratic equations.
• Circa 850: Indian mathematician Mahavira solves various quadratic, cubic, quartic, quintic and higher-order equations, as well as indeterminate quadratic, cubic and higher-order equations.
• 1114: Indian mathematician Bhaskara, in his Bijaganita (Algebra), recognizes that a positive number has both a positive and negative square root, and solves various cubic, quartic and higher-order polynomial equations, as well as the general quadratic indeterminant equation.
• Circa 1400: Indian mathematician Madhava of Sangamagramma finds iterative methods for approximate solution of non-linear equations.

## Modern Contributions

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