Indian Mathematicians and their Contributions – Overview

Approximation of the square root of 2. He proposed the he statement version of the Pythagorean Theorem.

Varttika, Vyakarana, later Sulba Sutras.

Matrameru, binary numeral system, arithmetical triangle.

Aryabhaṭiya, Arya-siddhanta

Pancha-Siddhāntikā, Brihat-Samhita, Brihat Jataka

Wrote of the book Tiloyapannatti. It gives various units for measuring distances and time. Different concepts about infinity.

Zero, Brahmagupta’s theorem, Brahmagupta’s identity, Brahmagupta’s problem.

Sine approximation formula.

Rule for finding the volume of a sphere.

Highly approach to algebra. Emphasis on developing the techniques that are necessary to solve algebraic problems.

Translated Ganitasara Samgraham into Telugu as Sara Sangraha Ganitamu.

Principles of differential calculus. Application to solve the astronomical problems.

Arithmetical treatise also known as Ganita Kaumudi. The Algebraic treatise called Bijganita Vatamsa.

Discovery of power series expansions of trigonometric functions; Notable works include Golavada, Madhyamanayanaprakara, Venvaroha.

He discovered the drk-ganita. It is a mode of astronomy observations.

Notable works include Golasara, Candrachayaganita, Aryabhatiya-bhashya, Tantrasamgraha, Raghunatha Siromani.

Notable works include Yukti-dipika, Laghu-vivrti, Kriya-kramakari.

Known for authorship of Yuktibhāṣā and Drkkarana.

Produced accurate sine tables.

He proposed the combination of traditional Indian astronomy with Aristotelian physics and Ptolemaic astronomy.

Notable works include Siddhanta-samrat, Yantra-prakara.

Calculated height of Mount Everest.

Known for Naked eye astronomy.

Established the culture of organised mathematical research in India.

Known for various contributions including Landau–Ramanujan constant, Mock theta functions, Ramanujan conjecture, and more.

Mahalanobis distance, Feldman–Mahalanobis model.

Pillai’s conjecture, the Pillai’s arithmetical function and the Pillai prime.

Known for various contributions including Association scheme, Bose–Mesner algebra, Euler’s conjecture on Latin squares, and more.

Known for multivariate analysis.

Known for various contributions including Chandrasekhar limit, Chandra X-ray Observatory, and more.

Known for Euler’s conjecture.

Known for Vaidya Metric, Vaidya–Patel solution, Einstein field equations.

Known for Pearson product-moment correlation coefficient, Vidyasagar University.

Cramér–Rao bound, the Rao–Blackwell theorem, the Orthogonal arrays and Score test.

Known for various contributions including Harish-Chandra’s c-function, character formula, homomorphism, and more.

Bahadur efficiency, the Anderson–Bahadur algorithm, the Bahadur-Ghosh-Kiefer representation, etc.

Known for Fisher consistency.

Known for Abhyankar’s conjecture, lemma, Abhyankar–Moh theorem.

Known for Seshadri constant, Narasimhan–Seshadri theorem, standard monomial theory.

Known for various contributions including power law inflation in Brans–Dicke theory, Theory of integrated tracking of quintessence fields, and more.

Known for Quantum stochastic calculus.

Known for Trombi–Varadarajan theorem.

Known for Combinatorial design and Graph Theory.

Known for Martingale problems, large deviation theory.

Known for Reproducing Kernels and Operators with a Cyclic Vector.

Frequency partition, different Line graphs and Degree sequences.

Known for Combinatorics and Graph Theory.

Developed the Non-commutative Iwasawa theory. Also worked on the Arithmetic of Algebraic varieties.

Known for Karmarkar’s algorithm.

Known for AKS primality test.

Known for Proof of Serre conjecture.

Known for Unique games conjecture.

Provided a counter-example over a field of positive characteristic to the special Zariski Cancellation Problem.