Harish Chandra, and the semisimple Lie in mathematics

Harish Chandra said his lack of training in math was actually an asset, because "knowledge, by advocating caution, tends to inhibit the flight of imagination".

Among the most prestigious awards in the field of mathematics is the Frank Nelson Cole Prize given by the American Mathematical Society in recognition of notable research work in algebra that has been published in a recognized and peer-reviewed venue. In 1954, the prize was given to Indian mathematician Harish Chandra for his work - in particular for his paper on some applications of the universal enveloping algebra of a semisimple Lie.

It was a complex piece of work, difficult for commoners to follow. But by linking algebra, analysis, geometry, and group theory, it became the cornerstone for much of the modern work in areas like differential geometry, mathematical physics and number theory.

The complexity is understandable since Harish Chandra, born 100 years ago in 1923, was a polymath in the truest sense of the term. Considered one of the outstanding mathematicians of his generation and certainly one of the greatest India has produced, Chandra graduated from the University of Allahabad where he studied theoretical physics before going on to do his postgraduate research on problems in theoretical physics under Homi Bhabha, at the Indian Institute of Science at Bangalore. His interest in physics was kindled after he stumbled upon Paul Dirac’s influential monograph Principles of Quantum Mechanics in the university library. Subsequently, when in 1945 he went to Cambridge for his PhD, it was under Dirac that he did his research.

But while he completed his doctorate in physics, he was intrigued by the possibilities in mathematics after attending lectures by British mathematician John Edensor Littlewood, whose students included the math wizard Srinivasa Ramanujan, and Marshall Hall, the American mathematician well known for his work in group theory and combinatorics.

Legend has it that at this time, Chandra also attended a lecture by Wolfgang Ernst Pauli, the Nobel Prize-winning Austrian theoretical physicist who was one of the pioneers of quantum physics. During the lecture the boy from Allahabad pointed out a mistake in Pauli's work, and thus started a life-long friendship.

After working for a couple of years as a physicist in Bangalore and Cambridge, Chandra moved with Dirac to Princeton University in the US, but by now his heart was not in physics. Instead, he found new inspiration in the work of mathematicians like Hermann Klaus, Austrian Emil Artin, renowned for his work on algebraic number theory, as well as Claude Chevalley, the Frenchman who made important contributions to number theory and algebraic geometry. From Princeton, Chandra went to Harvard University, where he was deeply influenced by the ideas of Oscar Zariski, the Russian-born American mathematician considered one of the greatest algebraic geometers of the 20th century.

These influences had a profound impact on Chandra, leading him to the conclusion that he “did not have the mysterious sixth sense which one needs in order to succeed in physics and I soon decided to move over to mathematics.” Then started what was the most productive phase of this brilliant man’s life as he joined the faculty of Columbia University. In between, he also went to the Tata Institute of Fundamental Research for a couple of years and was also a Guggenheim Fellow in Paris and a Sloan Fellow. Eventually, he was named the IBM von Neumann Professor of Mathematics at the Institute for Advanced Study in Princeton from 1961 to 1963.

By now his work on developing a fundamental theory of representations of Lie groups and Lie algebra was hailed as pathbreaking. The many laurels that came his way over the years including being elected a fellow of the Royal Society in 1973 and a member of the National Academy of Sciences of the US in 1981.

Equally rewarding is an understanding into his insight that the lack of background in mathematics was in a way responsible for the novelty of his work. As he explained: “I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naiveté, unburdened by conventional wisdom, can sometimes be a positive asset.”