In 1963, Harish Chandra was invited to become a permanent member of the Institute of Advanced Study in Princeton and in 1968 , he was named IBM Von Neumann Professor of Mathematic. He was Fellow of both the Indian Academy of Sciences and the Indian National Science Academy. He was elected to the Royal Society in 1973 and later to other academies as well . He gave invited plenary addresses at the International Congress of Mathematicians in Amsterdam in 1954 and in Moscow in 1966. For a man of his accomplishments, he received relatively few awards and honors though.
I had the privilege of a little personal acquaintance with Harish Chandra . During the year I spent Princeton, I met and talked to him several times. Unfortunately, I never interacted with him mathematically, but had numerous interesting conversations about mathematics. He made a strong impression on me and came through as an intense person with an austere outlook. He had strong views on mathematics and the mathematical scene in India. He was forthright in expressing them. After that year in Princeton, my meetings with him were far and few between. In October 1983 , I was again in Princeton to participate in a conference to honour Armand Borel (the only mathematician who has collaborated with Harish Chandra and a colleague of his at the Institute for Advanced Study.) On the last day of the conference , I was at a luncheon party hosted by Harish Chandra and his gracious wife (Lalitha had become Lily in Princeton ) - he had turned sixty just the previous week. Late that evening , I was to learn that Harish Chandra who had been at his lively best in the afternoon had died early in the evening. The week that began as a celebration of an outstanding mathematical intellect ended sadly , mourning the departure of another.
So far I have talked about men who were considerably senior to me in age! Now come to two outstanding names who were my contemporaries: C.P.Ramanujan and Vijay Kumar Patodi. When I joined TIFR as a student in 1960 Ramanujan was already there still a student, yet to take his degree. He had however, a formidable reputation as a versatile and deep scholar and an original mind. Expectations from him were such that there was a mild air of disappointment that he had not yet (at 22 ) come out with some creative work. He himself seemed to be in doubt about his abilities. But, in 1962 set at rest all anxiety on this count. He came up with a very nice result on cubic forms over algebraic number fields. And shortly there after, he gave a brilliant and remarkably simple proof of a much sought after result related to the Waring problem which I mentioned in connection with Pillai. It was a question that had interested Siegel greatly. After these initial forays into number theory, Ramanujan moved into algebraic geometry, where his contributions were again highly original and are valued greatly.
Many of us, his fellow students learnt a great deal of mathematics from Ramanujan and some of that in areas quite different from his own research interests. His scholarship was stupendous and his enthusiasm for mathematics was infectious. Learning from him was an exhilarating experience. He kept odd hours and many of our learning sessions with him would go late into the night . Ramanujan was widely read outside mathematics as well.
Ramunujan was without doubt one of the finest mathematical intellects to come out of India, but he was far from satisfied with his own achievements. Unfortunately, he came to be tormented as early as 1964 by an illness which was diagnosed as schizophrenia, with severe depression which interfered badly with his work. The malady would surface periodically, but in between, in periods of lucidity he would come up with beautiful results. Eventually, he ended his life in October 1974 during one of his bouts of depression. He was 36.
Ramanujan was mostly at TIFR during his short career, but visited several other mathematical centers . In fact, he took up a Professorship at Chandigarh in 1965. intending to stay there permanently. He was immensely liked by his colleagues and reciprocated their warmth, but illness struck an he left Chandigarh after just eight months. A six month visit to France on an invitation from the prestigious Institute des Hautes Etude Scientifiques had also to be cut short for similar reasons. He later spent some time at Warwick University in England and also at the University of Genoa in Italy. His colleagues in Genoa have fond remembrances of him a lecture hall in the Mathematics Department there was named after him after his death. At his request, he was relocated in Bangalore by TIFR and he spent the last year of his life there.
Ramanujan was mostly at TIFR during his short career, but visited several other mathematical centers . In fact, he took up a Professorship at Chandigarh in 1965. intending to stay there permanently. He was immensely liked by his colleagues and reciprocated their warmth, but illness struck an he left Chandigarh after just eight months. A six month visit to France on an invitation from the prestigious Institute des Hautes Etude Scientifiques had also to be cut short for similar reasons. He later spent some time at Warwick University in England and also at the University of Genoa in Italy. His colleagues in Genoa have fond remembrances of him a lecture hall in the Mathematics Department there was named after him after his death. At his request, he was relocated in Bangalore by TIFR and he spent the last year of his life there.
Just two years after the loss of Ramanujan , in December 1976 , Indian mathematics suffered another big blow. Vijay Kumar Patodi, a star still on the rise was cruelly cut-off at the age of 31. Patodi graduated from Benares Hindu University in1966 and after a year as a research scholar at Bombay University joined TIFR , to Continue working for doctorate. He had been taking courses at TIFR even while he was student at the university and it was obvious to his teachers
that he was exceptional. Patodi absorbed rapidly a lot of deep and difficult mathematics. Towards the end of 1969 , he came across a paper of Mckean and Singer and quietly started working on a conjecture stated in the paper . The paper made use of the profound work of Minakshsundaram on the Replacing on compact manifolds. The main thrust of the conjecture was to offer alternative approach to the classical Gauss-Bonnet theorem. A few months later, Patodi settled the conjecture and the announcement came as a total surprise to everyone at TIFR. The paper appeared in1971 in the Journal of Differential Geometry, and it was big news. Patodi received many invitations and visited Singer at MIT and later Atiyah at the Institute for Advanced Study. He developed further the ideas and techniques of his first paper, to obtain many interesting results; and all this culminated in a collaboration with Atiyah and Bott, where they were able to give a proof of the famous Atiyah-Singer index theorem by the heat equation techniques suggested in the Mckean-Singer paper.
In the midst of his great professional success, there was unfortunately terrible news. He was informed by his doctor that he had a serious medical condition and the prognosis was far from optimistic. Even while fighting hard to keep his illness at bay, Patodi kept at his mathematics and was producing excellent work. The end came in December 1976, shortly before a planned kidney transplant. In the short period of six years, despite frequent interruptions because of his illness, Patodi produced eleven papers of superb quality. Some of these papers appeared in print, posthumously.
that he was exceptional. Patodi absorbed rapidly a lot of deep and difficult mathematics. Towards the end of 1969 , he came across a paper of Mckean and Singer and quietly started working on a conjecture stated in the paper . The paper made use of the profound work of Minakshsundaram on the Replacing on compact manifolds. The main thrust of the conjecture was to offer alternative approach to the classical Gauss-Bonnet theorem. A few months later, Patodi settled the conjecture and the announcement came as a total surprise to everyone at TIFR. The paper appeared in1971 in the Journal of Differential Geometry, and it was big news. Patodi received many invitations and visited Singer at MIT and later Atiyah at the Institute for Advanced Study. He developed further the ideas and techniques of his first paper, to obtain many interesting results; and all this culminated in a collaboration with Atiyah and Bott, where they were able to give a proof of the famous Atiyah-Singer index theorem by the heat equation techniques suggested in the Mckean-Singer paper.
In the midst of his great professional success, there was unfortunately terrible news. He was informed by his doctor that he had a serious medical condition and the prognosis was far from optimistic. Even while fighting hard to keep his illness at bay, Patodi kept at his mathematics and was producing excellent work. The end came in December 1976, shortly before a planned kidney transplant. In the short period of six years, despite frequent interruptions because of his illness, Patodi produced eleven papers of superb quality. Some of these papers appeared in print, posthumously.
All the people I have spoken about so far are no more. The next person I am going to talk about, K.Chandrasekharan, is living in retirement in Zurich, Switzerland. He was born in 1920 and was initiated into mathematics by-who-else-Ananda Rao in Madras. He went to the Institute for Advanced Study in Princeton to do post doctoral work. Chandrasekharan worked in number theory and summability- like many others of his generation. His mathematical achievements are of the first rank, but his even greater contribution to Indian mathematics, I think, lies elsewhere. He was an extraordinarily gifted organizer and administrator of science- in the Bradman class, if we use Hardy's terminology. Homi Bhabha visited Princeton in 1949 when Chandrasekharan was there and offered him a position at the Tata Institute of Fundamental Research. There is a story about this which I have not authenticate, but it rings true. Chandrasekharan was taking a walk with the great Von Neumann when they saw BhaBha walking with Einstein at a distance. Von Neumann asked Chandrasekharan if it was true that he was planning to move to Bombay to work at Bhabha 's Institute. When Chandrasekharan responded in the affirmative, Von Neumann said, 'That man is as good a physicist as any, but do not let him intimidate you-stand up to him,' or words to that effect. It would appear that KC as Chandrasekharan was known, followed that advice- differences of opinion with Bhabha seen to have been among the causes that led to his leaving TIFR in 1965 and move to Zurich.
I should like to tell you another anecdote relating to KC, which I have first hand knowledge. This again goes back to my Princeton visit in 1966-67. I once accompanied a friend with expensive tastes to a clothing shop in Princeton. My friend ordered a suit for himself, while I acquired a scarf (which cost me 16 dollars in 1966, mind you) . The shopkeeper who kept up a conversation right through asked us if we knew Von Neumann and we said that we knew of him. Then he asked us if we knew Chandrasekharan and we told him that we did indeed know him; at which point he said, 'They are the only two gentleman from that Institute who knew how to dress!
I should like to tell you another anecdote relating to KC, which I have first hand knowledge. This again goes back to my Princeton visit in 1966-67. I once accompanied a friend with expensive tastes to a clothing shop in Princeton. My friend ordered a suit for himself, while I acquired a scarf (which cost me 16 dollars in 1966, mind you) . The shopkeeper who kept up a conversation right through asked us if we knew Von Neumann and we said that we knew of him. Then he asked us if we knew Chandrasekharan and we told him that we did indeed know him; at which point he said, 'They are the only two gentleman from that Institute who knew how to dress!
In the decade and a half that he spent at TIFR, Chandrasekharan transformed the fledgling School of Mathematics there into a center of excellence, respected the world over Chandrasekharan initiated a very successful programme of recruitment and training of Research Scholars at TIFR: the progamme continues to this day , along the same lines that he set down. He was uncompromising in insisting on high standards. In his Princeton days, he became acquainted with many of the leading mathematicians of the world and put these contacts to excellent use. Herman Weyl gifted his collection of Mathematics Annalen volumes to the TIFR, thanks to Chandrasekharan. With his unusual abilities, he was able to persuade many leading mathematical figures to visit the Tata Institute and deliver courses of lectures over a period of two months and more, to his carefully selected Research Scholars. Among the many distinguished men who visited the Tata Institute in the fifties, two names stand out: L.Schwartz - a Field Medalist- and C.L.Seige. They both had tremendous influence on the way mathematics evolved at TIFR. Schwartz persuaded many of his colleagues and students to visit the Tata Institute. Research Scholars were asked to write notes for the lectures given and these lecture notes enjoy a great reputation in the mathematical community to this day.
Chandrasekharan was an excellent judge of mathematics even in areas outside his own specialization, and responded quickly to the achievements of his wards. Equally, non performance at the high level he had set had no place at TIFR. Chandrasekharan managed to instill in the students at TIFR, strong commitment to hard work without their losing their romantic attachment to mathematics . One important reason for his success was the freedom he gave the students to work on what they pleased. The visitors gave them exposure to different mathematical areas, many of them for removed from KC's own interests, and students were encouraged to pursue whatever caught their fancy. Rev.Father Racine from Madras whom Chandrasekharan knew from his Madras days and whom he held in great respect, provided him with a steady stream of talent.
Chandrasekharan was ably assisted in his endeavors by K.G.Ramanthan. A student of Racine's Ramanathan too was in Princeton for post doctoral work. There , he came under the influence of E.Artin-another 20th century's major figures- and even more, Siegel. Through him, many TIFR were exposed to some of Siegel 's profound works, and this is very much reflected in the work that came out of TIFR in the sixties and seventies. Ramanathan was also responsible -during the seventies and eighties- for building a small but highly competent group in Partial Differential Equations- an area of great importance in applications. The group was located in the campus of the Indian Institute of Science in Bangalore, with a view to foster with that institution. Ramanathan passed away in 1992.
Chandrasekharan's influence went well beyond Indian mathematics for some 24 years from the mid-fifties. He was a member of the Executive Committee of the International Mathematical Union-IMU- He also served as the Secretary for two terms and as President for one term. His initiatives on this committee were numerous and valued greatly. He was responsible for the IMU sponsoring the International Mathematical Colloquium held once every four years at the Tata Institute starting 1956. These meetings have been on diverse topics in mathematics, topics that are of current substantially . They have been a great success over the years and an invitation to the meeting is considered prestigious.
I should like to mention a personal experience in this connection. In 1964 Tata Institute held a Colloquium on 'Differential Analysis' and the organizing committee headed by Chandrasekharan extended an invitation to me to give a talk . A few weeks before the colloquium, I was told that I should rehearse my lecture before KC in his office. My teacher Narasimhan was also present at the rehearsal. Chandrasekharan's own mathematical interest had little to do with the suvject of my talk; never the less, he listened to me patiently for more than an hour, interjecting now and then to tell me how I should present something and generally giving me tips on lecturing. I had in those days , a reputation as a poor speaker- which I hope does not hold now - but as it turned out, thanks to Chandrasekharan, I gave a lecture that was received very well indeed.
In the fifties , Chandrasekharan held the editorship of Journal of the Indian Mathematical Society. During this period, several great papers appeared in the journal thanks to Chandrasekharan's abilities at persuading some of the great names in the field to publish there.
We at the Tata Institute certainly owe a great deal to Chandrasekharan and are grateful for the great start he gave us
Based on a public lecture delivered at the Annual Meeting of the Indian Academy of Sciences, held at Chandigarh in 2002.
M.S. Raghunathan is in the Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai 400-005, India e-mail: msr@math.tifr.res.in
