Harish-Chandra was born on 11 October, 1923 in Kanpur, an industrial town near Prayagraj (Allahabad) in Uttar Pradesh, India. He became one of the leading mathematicians of the twentieth century. Harish-Chandra died on 16 October, 1983, in Princeton, New Jersey, USA. The following biography of Harish-Chandra, by John J. O'Connor and Edmund F. Robertson, and the accompanying photograph, are from the MacTutor History of Mathematics Archive, at the University of St. Andrews, Scotland.
Harish-Chandra attended school in Kanpur, then attended the University of Allahabad. Here he studied theoretical physics, this direction being the result of studying Paul Dirac's treatise  on quantum mechanics. He was awarded a master's degree in 1943, and then went to Bangalore to work further on theoretical physics. After a short while, Harish-Chandra went to Cambridge, where he studied for his Ph.D. under Dirac's supervision. During his time in Cambridge, he moved away from physics, and became more interested in mathematics. While at Cambridge, he attended a lecture by Pauli, and pointed out a mistake in Pauli's work. The two were to become life long friends. Harish-Chandra obtained his degree in 1947 and, in the same year, he went to the USA. Dirac visited Princeton for one year, and Harish-Chandra worked as his assistant during this time. However, he was greatly influenced by the mathematicians Hermann Weyl and Claude Chevalley. The period from 1950 to 1963 was his most productive, and he spent these years at the Columbia University. During this time, he worked on representations of semisimple Lie groups. Also, during this period he had close contact with André Weil. In , Harish-Chandra is quoted as saying that he believed that his lack of background in mathematics was, in a way, responsible for the novelty of his work:
Harish-Chandra worked at the Institute for Advanced Study at Princeton from 1963. He was appointed IBM von Neumann Professor in 1968. He died of a heart attack at the end of a week long conference in Princeton, having earlier suffered from three heart attacks. Harish-Chandra received many awards in his career. He was a Fellow of the Royal Society of London, and a Fellow of the National Academy of Sciences. He won the Cole prize from the American Mathematical Society in 1954 for his papers on representations of semisimple Lie algebras and groups, and particularly for his paper . In 1974, he received the Srinivasa Ramanujan Medal from the Indian National Science Academy.