At Princeton he took courses from esteemed mathematicians Emil Artin, Claude Chevalley, and Hermann Weyl. In 1949-50, he spent a year at Harvard to study algebraic geometry with Oscar Zariski. Harish-Chandra then became a professor at Columbia in New York (1950-63) before returning to the Institute for Advanced Study, where he remained for the rest of his life as the IBM-von Neumann Professor of Mathematics. Harish-Chandra’s years at Columbia were his most productive, mathematically, as he concentrated on the discrete series representations of semi-simple Lie groups. He is also known for his work with Armand Borel founding the theory of arithmetic groups. Before changing from physics to mathematics, he had already written a paper on infinit -dimensional representations of semisimple and reductive groups, which were not of much use in physics but had a great deal of significance in mathematics. Despite having some gaps in his mathematical background, he made up for those with his creativity and work-ethic to invent the tools he needed as ‘scaffolding’ for his research,at times unaware that they existed in formal literature. He was among those responsible for transforming infinite-dimensional group representation theory from a topic found on the periphery of mathematics and physics into a major field at the heart of leading-edge mathematics. Eventually, mathematicians moved away from the problem of solving equations to the study of the abstract groups. One problem they faced was to represent abstractly formulated groups by concrete means. With the rise of quantum mechanics infinite groups and matrices had to be considered. To understand very complex interacting systems of highly energetic elementary particles it is necessary to study the group of symmetries that leave the system unchanged. The groups that are most important to this problem are known as simple groups. Harish-Chandra constructed the most fundamental infinite dimensional representations of all of the simple groups and used them to represent generalized functions in these groups by means of Fourier series. Besides high-energy physics, applications of representation theory of simple groups are found in modern number theory and Galois Theory.

Harish-Chandra once attempted to express his mathematical aesthetics in a painting metaphor, “In mathematics there is an empty canvas before you which can be filled without reference to external reality.” This statement aptly sums up the fundamental aims and nature of pure mathematics. Harish-Chandra, whose health had always been fragile, had his first heart attack in 1969, and from then on his health was a major concern. He suffered a fatal heart attack on October 16, 1983 as he walked in the woods near the Institute. He was considered for the Fields Medal in 1958, but due to internal dissensions among certain mathematicians toward what they termed was ‘Bourbakist’, he was set aside. Nonetheless he was the recipient of the Cole Prize, a Fellow of The Royal Society, and many other honours and accolades.