Mudumbai Seshachulu Narasimhan, a towering figure in Indian science, passed away on May 15 in Bangalore; he would have turned 89 on June 7.
He was a world-renowned mathematician of extraordinary breadth and depth, who made fundamental contributions to diverse fields in mathematics such as algebraic geometry, differential geometry, representation theory and partial differential equations.
Born in 1932 in a family of agriculturalists in Tandarai village in northern Tamil Nadu, Narasimhan had a keen interest in mathematics from his school days. In an interview with mathematician Sujatha Ramdorai for Asia Pacific Mathematics Newsletter , he said that when he was 12, he was fascinated by Euclid and solving “riders,” thinking for oneself.
When asked about the moments he cherished in his life, his answer was: “The best moments, I think, were the times I spent as a student with Father Racine, K. Chandrasekharan and L Schwartz, which shaped my approach to mathematics and my mathematics career.”
In Loyola College, Chennai, Father Racine, a Jesuit priest and a student of Elie Cartan, noticed the talent of young Narasimhan and asked him to take up higher studies in mathematics at Tata Institute of Fundamental Research (TIFR) in Mumbai, where a school of mathematics had just been founded by K. Chandrasekharan.
Narasimhan went to TIFR for his PhD in 1953 and among his co-students was C.S. Seshadri, with whom he went on to collaborate closely. Narasimhan and Seshadri shot to fame in 1965 with the publication of the Narasimhan-Seshadri theorem, which makes a deep and unexpected connection between two different areas of modern mathematics. This and the Harder-Narasimhan filtration (which was discovered later with German mathematician G. Harder) have been generalised and stand as fundamental examples of paradigms with wide applicability.
Narasimhan and Seshadri continued to be good friends, and the former was a great support when Seshadri established the Chennai Mathematical Institute.
One of Narasimhan’s PhD students and mathematician at Chennai Mathematical Institute, Prof. T. R. Ramadas, says in an article in Current Science , “Mathematical theorems are rarely described as discoveries. When they were barely 30 years old, Narasimhan and Seshadri made a remarkable discovery at the cross roads of Algebraic Geometry and Complex Analytic Geometry of that era.”
Prof. Ramadas joined TIFR to do a PhD in physics and he describes how he crossed over to mathematics in the article. Following a series of lectures given by Narasimhan on vector bundles, connections and characteristic classes, Prof. Ramadas, who was a note-taker, ended up in discussions with the former.
“Over the next two years, I reported to Narasimhan my attempts to understand Gauge Theories … and Dirac’s theory of constrained systems. Then, I watched in awe as he laid bare the geometry underlying the theory, in work that became the body of my thesis,” says Prof. Ramadas.
Many of Narasimhan’s students acquired renown in the field — they include S. Ramanan, M. S. Raghunathan, V. K. Patodi and R. Parthasarathy.
Lingering advice
In his article, Prof. Ramadas mentions that though Narasimhan was spare with advice, some of his aphorisms and advice continued to linger. Some of this is paraphrased here: (1) While learning new mathematics, do not spend too much effort on hard exercises; save your energy for research problems. (2) Understand simple cases first. (3) Learn and think about any piece of mathematics from the most advanced/sophisticated point of view you are capable of. (4) Administration is important. (5) You have been helped by those who went before, so you should help those who come after. (6) In the beginning of the workday, sit and do some relatively concrete mathematics – say compute a homotopy group – even if your work is going nowhere. If you are lucky enough to be in the midst of a project with its own momentum, contrive to end the day with a concrete task programmed for the next day.
Narasimhan was with the mathematics department at TIFR for the large part of his career. From 1992-1999, he was head of the Mathematics group at the International Centre for Theoretical Physics at Trieste, Italy, and then moved to Bangalore, where he resided. He won the S.S. Bhatnagar prize in 1975, Third World Academy award for mathematics in 1987, Padma Bhushan in 1990, Fellow of the Royal Society and King Faisal International Prize for Science in 2006 (jointly with Simon Donaldson, Imperial College).
Narasimhan was married to Sakuntala Narasimhan, a musician, journalist and consumer advocate. Their daughter and physicist Shobhana Narasimhan is at JNCASR, Bengaluru, and son Mohan is a management professional in Bengaluru.
