WILLIAM  TIMOTHY  GOWERS

                              Sir William Timothy Gowers, FRS (born 20 November 1963) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.
  
                             Gowers has written several works popularising mathematics, including
 Mathematics: A Very Short Introduction (2002), which describes modern mathematical research for the general reader. He was consulted about the 2005 film Proof, starring Gwyneth Paltrow and Anthony Hopkins. He edited The Princeton Companion to Mathematics (2008), which traces the development of various branches and concepts of modern mathematics. For his work on this book, he won the 2011 Euler Book Prize of the Mathematical Association of America.

             MICHAEL  ATIYAH  CONTRIBUTION  TO

                               MATHEMATICS

           “One of the world's greatest living mathematicians, Sir Michael Atiyah has made fundamental contributions to many areas of mathematics, but especially to topology, geometry and analysis. From his first major contribution—topological K-theory—to his more recent work on quantum field theory, Sir Michael has been influential in the development of new theoretical tools and has supplied far-reaching insights. He is a notable collaborator, with his name linked with other outstanding mathematicians through their joint research. A superb lecturer, he possesses the ability to explain sophisticated mathematics in a simple geometric way.”

From the Abel Prize Foundation:

“The second Abel Prize has been awarded jointly to Michael Francis Atiyah and Isadore M. Singer. The Atiyah-Singer index theorem is one of the great landmarks of twentieth-century mathematics . . . . the culmination and crowning achievement of a more than one-hundred-year-old evolution of ideas, from Stokes’s theorem, which students learn in calculus classes, to sophisticated modern theories like Hodge’s theory of harmonic integrals and Hirzebruch’s signature theorem. The problem solved by the Atiyah-Singer theorem is truly ubiquitous. In the forty years since its discovery, the theorem has had innumerable applications, first in mathematics and then, beginning in the late 1970s, in theoretical physics: gauge theory, instantons, monopoles, string theory, the theory of anomalies, etc.”

               TERENCE TAO- MATHEMATICIAN

WORKS IN MATHEMATICS:

                                Terence Tao has done work in many different fields of mathematics (although as you can assume from Paul's focus on Tao's number theory work, arguably his most profound contributions have been in that field). Terence Tao specializes in partial differential equations, analytic number theory, harmonic analysis, combinations, matrix theory and ergodic theory. The actual contributions he has made are mainly in number theory, like the Green-Tao theorem, but he has made many other advances in many of the aforementioned fields, they are just not as profound as the Green-Tao theorem and some of his other working in number theory. Terence Tao is a mathematical genius by all definitions (also a genius in most other fields of academia), he has mastered most of the concepts in mathematics and has done research for many years in an attempt to better our understanding of the world through mathematics. The only way that I can truly stress the influence he has had in mathematics, without you having to understand any of the mathematics is to say that he won the Fields Medal, which is considered the "Nobel Prize of Mathematics" and is only awarded every four years.

                              C.S. SESHADRI

                       C.S. Seshadri FRS (born 29 February 1932) is an eminent Indian mathematician. He is the founder and Director-Emeritus of the Chennai Mathematical Institute, and is known for his work in algebraic geometry. The Seshadri constant is named after him.
He is a recipient of the Padma Bhushan in 2009,the third highest civilian honor in the country. Research work:

                Seshadri's main work is in algebraic geometry. His work with M S Narasimhan on unitary vector bundles and the Narasimhan–Seshadri theorem has influenced the field. His work on Geometric Invariant Theory and on Schubert varieties, in particular his introduction of standard monomial theory, is widely recognized. Seshadri's contributions include the creation of the Chennai Mathematical Institute, an institute for the study of mathematics in India.

                   NARENDRA  KARMARKAR

Karmarkar’s Famous algorithm

                           Karmarkar’s algorithm solves the various linear Programming problems in the polynomial time. These problems are mostly represented by a “n” variables and a “m” constraints. The previous used method for solving these type of problems consisted a lot of problem representation by a “x” sided solid with a “y” vertices, where all the solution was then approached by traversing it from the vertex tovertex. Karmarkar’s novel method approaches all the solution by method of cutting through the all the above solid in all its traversal.        

                      Consequently, the complex optimization problems are also solved much faster using the method of Karmarkar algorithm. A practical example of this type of efficiency is the solution to a very complex problem in the communications network optimization where all the solution time taken was reduced from the weeks to some days. His algorithm thus enables the faster business and various policy decisions. Karmarkar’s algorithm has also stimulated all the development of the several other used interior point methods, some of which are now used in the current codes for solving the linear programs.

                          HARISH  CHANDRA

CONTRIBUTION TO MATHEMATICS:

                The word mathematics is like a dangerous monster for some people. Many of the students who consider mathematics as their enemy would have thought that the subject mathematics should never have existed. But in this world of billions of population, there are many who not only love mathematics but take it up as their career.

Harish Chandra was one among such people in the olden times who was a well-known mathematician. Not only did he like the subject mathematics, but also made significant contributions to the world of mathematics which is undoubtedly praiseworthy. Harish Chandra was born on 11th of October, 1923 in Kanpur. He belonged to an upper middle class family which was a benefit to the educational career of Harish Chandra.

    Harish Chandra researched on “Semi Simple Lie Groups”. This was indeed his best research. He explained about the lie algebra where the ideal of the number were 0 and itself. Other achievements of Harish Chandra include Weyl’s character formula analogue, Plancherel measure for semi simple groups, philosophy of cusp forms, etc. he also worked at Neumann Professor in 1968 at the Institute of Advanced Study.

               Harish Chandra was a great mathematician of the twentieth century. His achievements and contributions were praiseworthy. He was honoured with AMS Cole Prize in 1954 for his outstanding work ‘Representations of Semi Simple Lie algebras and groups’. He was the Fellow of the Royal Society. He was given the Ramanujan Medal in 1974 for his wonderful works in mathematics. Not only in India, but Harish Chandra’s achievements were honoured outside India as well. He was given an honorary degree in the Yale University. Harish Chandra Research Institute (HRI) was started by the Government of India in the honour of his contributions in the field of mathematics.

                       C.RADHAKRISHNA RAO

CONTRIBUTIONS TO STATISTICAL THEORY AND APPLICATIONS

                                       C. Radhakrishna Rao is among the world leaders in statistical science over the last six decades. His research, scholarship, and professional services have had a profound influence on theory and applications of statistics.

Technical terms such as, Cramer-Rao inequality, Rao-Blackwellization, Rao’s Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, Rao
metric and distance, Analysis of Dispersion (MANOVA) and Canonical Variate analysis and G-inverse of matrices appear in all standard books on statistics. Cramer-Rao Bound and Rao-Blackwellization are the most frequently quoted key words in statistical and engineering literature. Special uses of Cramer-Rao Bound under the technical term, Quantum Cramer- Rao Bound have appeared in Quantum Physics. Rao-Blackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks etc. These results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.

Rao has made some significant contributions to combinatorial mathematics for use in design of experiments, the most important of which is Orthogonal arrays (OA).The basic paper on the subject appeared in Proc. Edinburgh Math. Soc. (the referee of the paper reported that it is a fresh and original piece of work). The Japanese Quality Control Expert, G.Taguchi made extensive use of OA’s (described by Forbes Magazine as “new mantra” for industries), in industrial experimentation.
Rao defined a generalized inverse (g-inverse) of a matrix (singular or rectangular) and demonstrated its usefulness in the study of linear models and singular multivariate normal distributions.

He is the author of 14 books and about 350 research papers. Three of his books have been translated into several European and Chinese and Japanese languages