20th century mathematicians:
Srinivasa Aaiyangar Ramanujan :-

is undoubtedly the most celebrated Indian Mathematical genius. He was born in a poor family at Erode in Tamil Nadu on December 22, 1887. Largely self taught, he feasted on Loney's Trigonometry at the age of 13, and at the age of 15, his senior friends gave him Synopsis of Elementary Results in Pure and Applied Mathematics by George Carr. He used to write his ideas and results on loose sheets. His three filled notebooks are now famous as Ramanujan's Frayed Notebooks. Though he had no qualifying degree, the University of Madras granted him a monthly scholarship of Rs. 75 in 1913. A few months earlier, he had sent a letter to great mathematician G.H. Hardy, in which he mentioned 120 theorems and formulae. Hardy and his colleague at Cambridge University, J.E. Littlewood immediately recognised his genius. Ramanujan sailed for Britain on March 17, 1914. Between 1914 and 1917, Ramanujan published 21 papers, some in collaboration with Hardy. His achievements include Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan's identities in partition of numbers, work on algebra of inequalities, elliptic functions, continued fractions, partial sums and products of hypergeometric series, etc. He was the second Indian to be elected Fellow of the Royal Society in February, 1918. Later that year, he became the first Indian to be elected Fellow of Trinity College, Cambridge. Ramanujan had an intimate familiarity with numbers. During an illness in England, Hardy visited Ramanujan in the hospital. When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=13+123=93+103.
Unfortunately, Ramanujan's health deteriorated due to tuberculosis, and he returnted to India in 1919. He died in Madras on April 26, 1920.

Well known Indian mathematicians :

P.C. Mahalanobis : He founded the Indian Statistical Research Institute in Calcutta. In 1958, he started the National Sample Surveys which gained international fame. He died in 1972 at the age of 79.C.R. Rao : A well known statistician, famous for his "theory of estimation"(1945). His formulae and theory include "Cramer -Rao inequality", "Fischer -Rao theorem" and "Rao - Blackwellisation". D.R. Kaprekar (1905-1988) : Fond of numbers. Well known for "Kaprekar Constant" 6174. Take any four digit number in which all digits are not alike. Arrange its digits in descending order and subtract from it the number formed by arranging the digits in ascending order. If this process is repeated with reminders, ultimately number 6174 is obtained, which then generates itself. Harish Chandra (1923-1983) : Greatly developed the branch of higher mathematics known as the infinite dimensional group representation theory. Narendra Karmarkar : India born Narendra Karmarkar, working at Bell Labs USA, stunned the world in 1984 with his new algorithm to solve linear programming problems. This made the complex calculations much faster, and had immediate applications in airports, warehouses, communication networks etc.