Forgotten genius

Remembering K. Chandrasekharan (1920-2017), one of the leading mathematicians of the 20th century who played a seminal role in making TIFR a world-renowned centre for mathematics.

Published : Jun 07, 2017 12:30 IST

K. Chandrasekharan.

K. Chandrasekharan.

ON April 13, Komaravolu Chandrasekharan, one of the leading mathematicians of the 20th century, passed away in Zurich, Switzerland, at the age of 96. KC, as he was known to many, was a well-known figure in the scientific community in India in the 1950s and ’60s. This was the time when he headed the School of Mathematics at the Tata Institute of Fundamental Research (TIFR) in Mumbai (then Bombay). Under his stewardship, that school grew from the fledgling institution that it was in 1950 to a world-renowned centre for mathematics (that it continues to be today), all in the short space of a decade and a half. He left India in 1965 to take up a professorship in Zurich, and, with that, he has been virtually forgotten in this country despite his immense contribution to the organisation and promotion of mathematics (and science) in India during his TIFR years.

Chandrasekharan was born in Machilipattanam in Andhra Pradesh on November 20, 1920. His father was the headmaster of a school in the small town of Bapatla (also in Andhra Pradesh). After his school education in Bapatla, he moved to Chennai (then Madras) for higher studies and obtained his B.A. (Hons) degree in mathematics from the University of Madras through Presidency College in 1943. He then went on to pursue a PhD degree under the guidance of Professor Ananda Rau (a leading mathematician of the time) even as he worked as a part-time lecturer in Presidency College. He was awarded the PhD degree in 1946. Marshall Stone, a leading American mathematician, was visiting Madras—he was drawn to that city because of his interest in Indian music. He met KC there, and was impressed enough with the young man to arrange for him to go to the Institute for Advanced Study (IAS) in Princeton, United States, to work as assistant to the famous mathematician-physicist Hermann Weyl (IAS, a Mecca for mathematicians, is the institute where Albert Einstein was a permanent professor, as was Weyl).

Homi Bhabha, who was on a visit to the United States (essentially for the purpose of recruiting faculty for TIFR), met him in Princeton and offered him a position at TIFR. KC accepted the offer and joined TIFR as a Reader in July 1949. At the time of his joining TIFR, there were only two other mathematicians in the institute: F.W. Levy and D.D. Kosambi. Levy had fled Nazi Germany and was a professor at the University of Calcutta when Bhabha recruited him. Kosambi was at the Banaras Hindu University before moving to TIFR and around the time KC joined TIFR he was moving away from mathematics to historical research. KC rose rapidly in the ranks and he was appointed Deputy Director (Mathematics) in 1960. He was instrumental in restructuring TIFR so that it had two schools—the School of Mathematics and the School of Physics, with functional autonomy in all academic matters in the respective fields; he was also the (first) Dean of the School of Mathematics.

Exceptional career KC’s mathematical researches were in the areas of classical analysis (much of it in Summability) and Number Theory. There seems to be a revival in recent years of some interest in his papers on Dirichlet Series (written jointly with R. Narasimhan) that appeared in the prestigious Annals of Mathematics in the 1960s. He was among the finest Indian mathematicians of his generation. He wrote two books, both of which were well received. One, titled Fourier Transforms , had as co-author Salomon Bochner (of the University of Princeton), one of the big names of the 20th century. The other, Typical Means , was a joint work with Minakshisundaram, who was arguably the most gifted Indian mathematician of that generation. KC was the first recipient of the Bhatnagar Prize for Mathematics in 1959 and was also awarded the Padma Shri in the same year.

KC left TIFR in 1965 to take up a permanent professorship at the Eidgenossiche Technishe Hochschule (ETH), a premier scientific research institution located in Zurich. But his achievements in the short span of about 16 years that he spent at TIFR are truly impressive and have few parallels on the Indian scientific scene. After he joined the institute, mathematical activity at TIFR grew by leaps and bounds in the next few years, thanks to the diverse initiatives he took. One of these was the recruiting of K.G. Ramanathan, a fine mathematician with interests somewhat removed from those of KC himself. The most important of the initiatives was the creation of a mathematics graduate school broadly along the lines of those in universities in the West, yet differing from them in some ways to suit local (Indian) conditions. The students for admission to the graduate school were selected with great care, ensuring that they were highly talented.

As mentioned earlier, Levy left TIFR soon after KC joined and Kosambi showed no great enthusiasm for training students. With just himself and Ramanathan available for teaching, KC embarked on a programme to get a large number of visiting professors from abroad to give graduate courses to the students he had assembled. With the contacts he had made during his years in Princeton, he was able to persuade many leading mathematicians in Europe and the U.S. to visit Mumbai for extended periods of time and give graduate courses. The intellectual fare provided by the visitors ignited the minds of the brilliant students and resulted in outstanding research being produced in TIFR by the late 1950s. Two of these visitors, who rank among the 20th century’s greats, Siegel and Schwarz, had a particularly strong influence on the mathematics school. Both of them made several lengthy visits, during every one of which they gave graduate courses.

KC got his wards to take down notes of the graduate courses given by the visitors and published them after getting them vetted by these lecturers. TIFR continues this practice to this day, except that with its coming of age, the visitors are often there for collaborative research with the local faculty rather than to give graduate courses. These publications (known as the Mathematics Lecture Notes Series of TIFR) have a high reputation and even the ones dating back half a century to KC’s time at TIFR are much sought after even now by the international mathematics community: they have now been digitised and are available for free downloads on the TIFR website.

By the late 1950s, the graduate school was producing research work of high calibre and the standard of theses written at TIFR were comparable to those in leading institutions in the world. One major difference between the graduate school at TIFR and those in Western universities (and this was Bhabha’s rather than KC’s innovation) was that students were hired as “Research Assistants” on a scale with yearly increments and were members of the Provident Fund after an initial year of probation. They were given five-year contracts which could be extended indefinitely. The emphasis was on acquisition of wide and deep scholarship; while original research was certainly the prime expectation from the Research Assistants, there was no pressure for publication or even to write a PhD thesis within a stipulated time. Students often registered for a degree well after they had completed the research needed to get the degree. The students who performed well became faculty and were placed in a higher scale.

KC responded to good work from students as well as junior faculty with an alacrity not seen in our institutions of higher learning (and in this he had Bhabha’s unstinted support and, in fact, KC was following Bhabha’s lead): he promoted them to higher levels—there was no requirement that the candidate should have a PhD. Indeed, the bye-laws of the institute ensured that bureaucratic norms did not come in the way of promoting excellence. There was at least one case of a mathematician appointed as an associate professor without a PhD; and the promotion, in fact, skipped two grades! The mathematician (C.P. Ramanujam) had, of course, some outstanding research publications to his credit and one of them later fetched him a PhD degree. KC set very high standards for research: he was ruthless in weeding out mediocrity even while he was proactive in promoting excellence. His assessment of professional performance (done in consultation with colleagues and visitors) were by and large fair. However, some of the harsh decisions could have perhaps been implemented with greater compassion.

Major initiatives Another important initiative of KC was the organisation of a periodic (every four years) meeting at TIFR, which he named “International Colloquium”, which continues to this day. This is a closed-door meeting (open, however, to all TIFR faculty and students) of invited experts from all over the world on a specific topic chosen by the Mathematics faculty. The main factors that go into this choice are major developments in the area and a substantial contribution from TIFR mathematicians. The idea was conceived by KC and he also put in the necessary effort to implement it. He persuaded the International Mathematical Union (IMU) to sponsor these meetings and also got the Dorabji Tata Trust to fund them substantially. During his tenure at TIFR, three such conferences took place and he was the organiser-in-chief for all of them. He had a big role in the choice of the theme of the conferences (two of which were somewhat distant from his own interests).

The mathematical genius Srinivasa Ramanujan left behind a whole lot of notebooks in which he had jotted down many mathematical comments and formulas. KC conceived the idea of photocopying the notebooks (which were in the custody of the University of Madras) and publishing them, thereby giving the mathematical public access to some unpublished ideas of Ramanujan. As was his wont, he pursued the idea to its successful implementation, securing the cooperation of the university and obtaining the necessary financial support from the Dorabji Tata Trust.

KC was also responsible for the creation of the Department of Mathematics at the University of Mumbai in 1960 and getting Sharadchandra Shankar Shrikhande, a distinguished mathematician, to head it. Until that time, the university functioned largely as an examining body that awarded degrees, the teaching and research in most subjects being carried out in the affiliated institutions.

Bhabha, evidently, saw in KC a lot more than the superlative administrative skills he displayed. Bhabha made him a member of the Scientific Advisory Committee to the Cabinet, of which he himself was the Chair. That committee drew up the Scientific Policy Resolution of the Government of India. KC is widely believed to have drafted that document. Jawaharlal Nehru set up a committee to write a report on the debacle in the war against China in 1962. KC was a member of the committee and I was told that Bhabha was somewhat unhappy that he did not have advance information on that!

There is a mural by M.F. Husain that adorns the wall next to the library on the mezzanine floor at TIFR. Husain was commissioned to paint this mural as the winner of a competition. Bhabha had persuaded a number of artists to submit entries for the competition—the entries were scaled-down versions of what the artist would paint on the wall if commissioned. The only TIFR member on the jury of four appointed by Bhabha for the competition was KC, an indication of Bhabha’s regard for KC as a connoisseur of art (the other three were renowned art critics).

Awe-inspiring KC was a man of great sophistication and refinement. He was a much-admired man in TIFR and was second only to Bhabha at that; however, he inspired awe rather than affection. He was socially somewhat aloof. There were just a handful of people at TIFR who interacted with him in non-professional ways. At the professional level, his conduct was rather formal but impeccable; and he never allowed social acceptability or otherwise to interfere with his enthusiasm for professional excellence in a colleague. He dressed formally—he would always turn up in a suit at TIFR even on the hottest summer days. Colleagues wanting to meet him had to take an appointment. He spoke (always in English) in a deliberate measured accent which was neither British nor American but would not be recognised as Indian either. Most of us at TIFR formed certain impressions about him though we did not get close to him (we were inclined to believe that no one outside his immediate family ever got really close to him). The way he dressed and the way he conducted himself at the rare official parties suggested to us that he was a stickler for (Western) etiquette who could give a lesson or two to Emily Post!

He counted among his friends many of the 20th century’s great mathematicians: Weyl, John von Neumann, Stone, Schwarz, Andre Weil, Siegel (whose selected works, he edited), Georges de Rham, Heinz Hopf, Henri Cartan… to name a few. Henri Cartan came all the way from Paris to Mumbai for the inauguration of the present campus of TIFR by Nehru. Thanks to KC, Weyl’s personal collection of all the volumes of the journal Mathematische Annalen (beginning with the first volume) was bequeathed to TIFR. I have seen a letter written to KC by Weil in early 1965. Weil apparently knew that KC was planning to leave TIFR. In that letter, he writes that KC should seriously consider taking up the chairmanship of the Mathematics Department at the University of Princeton and seeks his permission to take up the matter with the President of the University (President Goheen was a good friend of KC’s). KC apparently told Weil that he was not interested in the Princeton job. Switzerland of the 1960s was far from keen on its prestigious institutions hiring foreign nationals. De Rham (a Swiss) had considerable influence with the Swiss government of the day and exerted it to get KC to ETH. De Rham evidently had high regard for KC as a mathematician.

TIFR made him an Honorary Fellow of the institute a year after he left, a gesture of recognition of his stature as a mathematician and his contributions to the institute.

KC’s contributions to the development of mathematics had an international dimension. The IMU is the oldest of all the international scientific unions—it had come into existence at the turn of the last century. However, it was largely a European organisation, with the U.S. and Canada playing somewhat limited roles. The functioning of the IMU in the period between the two World Wars was disrupted because of the souring of relations between French and German mathematicians.

Association with the IMU Stone initiated efforts to revive the IMU after the Second World War. He formed a committee to draw up revised statutes for the IMU. KC, who was roped into the committee by Stone, was apparently a major contributor in drafting the new statutes. He went on to serve a record 24 years on the executive committee of the (new) IMU, five of them as secretary and four as president. During his tenure as secretary, he formulated the rules for the conduct of the International Congress of Mathematicians (ICM), the principal event the IMU organises every four years; and the statutes he laid down in the mid 1960s for its conduct continue to be operative to this day. KC also played a significant role in bringing Soviet bloc countries into the IMU fold during the height of the Cold War. He steered the IMU into taking a great interest in promoting mathematical activities in developing countries. He also served on the International Council of Scientific Unions (ICSU) as secretary general and, at a later point, he was the president.

KC was at ETH until his retirement in 1988 and continued to live in Zurich until his death. While personal considerations were the primary reason for his quitting TIFR, he seems to have had differences with Bhabha on matters of policy, which may also have contributed to that decision. I expect that KC remained an Indian citizen until his death: I met him once in Zurich in the year 2000 (that was the last time I met him), when he told me that he was an Indian citizen at that time and that he had no intention of giving up that citizenship.

Personal anecdotes I will end this note recounting some anecdotes: they will perhaps throw more light on his colourful personality than all that I have said above.

I will begin with my own encounters with him. My first encounter was at the entrance interview for TIFR—he was the chair of the committee. He asked me a (mathematical) question, and I was struggling with it when he declared: “Ah, he must have mugged it all up and is unable to reproduce it here!” I was seething with anger but, of course, dared not show it. That was, in fact, the only intervention he made during that interview, and I went back with the impression that he was a bully.

After I joined TIFR, during the five years he was there, I met and spoke to him exactly thrice. The first experience was to reinforce my first impressions. KC was secretary of the IMU at that time and was responsible for the publication of the World Directory of Mathematicians , a publication that was essentially a listing of mathematicians (so determined by a specified criterion). KC got some members of the school to help him with this—their job was to go through the list of names provided by the member countries of the IMU and remove names that did not qualify. This was essentially a clerical job but it required some background in mathematics. It was the general feeling in the school that KC thought none too well of those whom he inducted into this job.

Sometime in 1962, I think, I was put on the job, along with three or four other colleagues. However, I paid no attention to it, and apparently, it did not get noticed until at one point of time all the others went away on vacation. I was summoned by KC and given a dressing-down for not doing the work assigned to me. I was already resentful about being put on the job and the dressing-down made it much worse. When I came out, I decided to quit TIFR and told some friends that I was quitting. They calmed me down and talked me out of taking precipitate action. Word must have reached KC soon after, conveying to him the general opinion of my colleagues and teachers that I was performing well in mathematics: within a week of that encounter, I was taken off the team that was assigned the World Directory work!

Pleasant encounters The next two encounters were pleasant. He called me to his office and told me that I was being promoted in response to some “good” work I had done. I mumbled an awkward thanks and got out of his office as quickly as I could. Naturally, I became better disposed towards him, but the idea of a bully would not yet disappear. In 1964, I was asked to speak at the International Colloquium held at TIFR. KC sent word to me that he would like me to rehearse my talk in the presence of himself and my teacher, M.S. Narasimhan. The subject matter of my talk was far removed from his interests. Nevertheless, he listened to me attentively and gave me several tips about the delivery. My talk was well-received: I had quite a reputation as a poor lecturer and so this took most colleagues by surprise. There is no question that KC’s tips were the decisive factor.

The next anecdote is a first-person account but is not about my interaction with KC. I was a visiting member, along with Raghavan Narasimhan, at the IAS in Princeton in 1966-67. On one occasion, the two of us went to a very expensive clothing shop (located on Palmer Square). Narasimhan ordered himself a suit while I acquired a scarf. The shopkeeper struck up a conversation with us and at one point asked us if we had known John von Neumann and when we replied that we only knew of him, he asked us if we knew “Chandrasekharaaan”. We answered in the affirmative, of course, when he said: “They were the only gentlemen from that Institute who knew how to dress!”

KC was once invited to give a colloquium talk at the University of Chicago. The usual practice in the mathematics departments is for some faculty member to go to the airport to receive the speaker and drive him/her to the department. On this occasion, all the faculty members were tied up with other engagements. The job of receiving KC at the airport was given to Mrs Kaplansky—Kaplansky was one of the members of the faculty. She set out to the airport with a baby daughter, who threw up on the way. Mrs Kaplansky cleaned up as well as she could and sprayed some perfume, which was not entirely effective in suppressing the bad smell. She got to the airport, received KC, brought him to the car and began apologising profusely for the smell, explaining how it had come about. KC put her at ease, assuring her that the perfume had taken good care of the smell, identified the perfume and engaged her in a conversation about perfumes all along the drive to the department! I heard the story from Mrs Kaplansky herself some 20 years after it happened. Evidently, she was charmed.

The third story is really hearsay—I do not remember who I got it from. When Bhabha was in Princeton to recruit KC, one day KC was taking a walk with von Neumann and just a little ahead of them Bhabha was walking with Einstein and Hideki Yukawa. Von Neumann apparently turned to KC and asked him if he was planning to take up Bhabha’s offer. When KC responded saying that he was considering it seriously, von Neumann told him: “That man is as good a physicist as any, but don’t let that intimidate you—stand up to him!” And if any one stood up to Bhabha any time in TIFR, it was KC.

Prof. M.S. Raghunathan is a former professor of mathematics at TIFR and is now at IIT Bombay in an emeritus position. As a student at the TIFR, he was witness to the School of Mathematics developing under K. Chandrasekharan.

Sign in to Unlock member-only benefits!
  • Bookmark stories to read later.
  • Comment on stories to start conversations.
  • Subscribe to our newsletters.
  • Get notified about discounts and offers to our products.
Sign in


Comments have to be in English, and in full sentences. They cannot be abusive or personal. Please abide to our community guidelines for posting your comment