One Hundred Tamils of the 20th Century Mamanithar C.Jeyaratnam Eliezer Prof C.J.Eliezer was honoured by the Federal Government with the Order of Australia and, in 1997 was awarded Tamil Eelam's highest national honour of "Maamathithar" by the Leader of Tamil Eelam, Velupillai Pirabaharan.
With Universities and with Mathematics - A Long Love Affair
Valedictory Address by Professor C.J.Eliezer
to Trobe University, Melbourne, December 1983 I have had a long innings as a University Academic. It is just over 45 years ago when, after completing an honours degree, I started lecturing at the University in Colombo, under an appointment similar to that of the present tutorship at La Trobe but with more lecturing duties. Since then I have moved along a long road which has taken me to several countries and universities. I had an early fancy that every 5 years or so I should change my place of work and every 20 years my profession. Things have not quite worked out that way, but I have had in all 8 years in Cambridge, 13 in Ceylon, 9 in Malaysia and nearly 16 at La Trobe - with sabbaticals in Princeton Institute, University of Chicago and Matscience in India. So in 4 continents, I have worked with hundreds of colleagues, sat in thousands of committees, worked on hundreds of research problems; taught tens of thousands of students, given tens of thousands of lectures, marked hundreds of thousands of examination scripts. My family and I have lived, among and enjoyed the friendships of people of various cultures, different nationalities, many language groups, and all major religious persuasions. We have found it easy to do so because of our upbringing where we learnt to repeat an ancient Thamil couplet of 2nd century B.C. (Puranaruru ): All the world is my homeland
All its people my kinsfolk.
Now reaching that age when formal professional life terminates and one looks back and reflects, two things about that professional life stand out: One is that I have been lucky to have as a abject one which is demanding and absorbing, one with a long history and which has profoundly influenced mankind and its ways, a subject which continues to grow and bring new surprises, a thing of beauty, elegance. intellectual challenges and emotional satisfaction, and occasionally, in those lucky moments, wild emotional, thrill. The second matter of luck for me was to work in universities in various stages of development, when much of the university world was expanding into a world wide community which valued and promoted a liberal education, and intellectual activity and growth, in an atmosphere of academic freedom where universities are not subject to political control or made instruments for particular power groups. At the same time universities have been moving towards a determination not to be isolated from the world at large. I was lucky to work in Universities when they were committed to the twin concepts of Autonomous University and a Responsible University. Thus the two worlds — the Mathematical world and the University world became early in life my professional loyalties, which with the passing of the years have mellowed into professional loves. This is the background to the title of my address. I had occasion about a year ago to speak on the Mathematical Sciences in Perspectives at the inauguration of the Institute of Fundamental Research in Sri Lanka (1982). I think that a summary of what I said then would be useful as introduction today. School Mathematics I am going to begin with some early history. In this audience, there are many mathematicians. I am going to suggest that every one here is or was a mathematician. Some would immediately disclaim that description. At school — one learnt about numbers and arithmetic. Later one learnt Geometry, with its theorems, construction and proofs. All that was good mathematics. How much lasting influence these had on each of us, we cannot really tell, not without psychoanalysis and study of the sub conscious . I would suggest that those influences were great, despite what our conscious memories may suggest. Some say of their school mathematics that they hated it. Bernard Shaw in his usual style had some pungent words. When late in life Karl Pearson convinced him of the use of statistics, he exclaimed that he realised only then that at school, instead of being taught mathematics, he had been made a fool of — with those x's, y's and other nonsense. Early History It is useful to recall the in the early history of man both numbers and geometry were integral parts of those processes which quickened human activity and led on to the beginnings and developments of what we call civilisation. That is, the origins of mathematics are intermingled with the origins of civilization. Certain evidences of our past have been buried in the debris of ancient cities or buried within ancient languages. In recent times archaeologists and linguists have combined to dig out information and to make interpretations. The picture they give is fascinating. Human activity quickened at the end of the last Ice Age. As temperatures began to rise, there was more fruit in the trees, and more fish in the streams. More food led to more population, which then began to cluster together for safer and better living, in villages than cities. The first cities emerged 10,000 years ago. However, the cities that came up about 5,000 — 6,000 years ago, on the banks of some great rivers, showed two new features: the invention of the wheel and development of writing. In Sumeria, on the banks of the Tigris and Euphrates, in Egypt on the banks of the Nile, in India in the Indus Valley, and in China near the Yangtze and Hwang-Ho, cities developed and human evolution had reached a new phase. The analysis of ancient languages has shown that in every major language, number words were an integral part of the evolution of that language. The words for the numbers were an integral part of the evolution of that language.... Before I conclude, I feel I ought to add some personal comments on these interests, and how l came by them. In Ceylon I had seen very good teachers and I had begun to like Mathematics —but it was in Cambridge when my interests took definite shape. Cambridge had a famous School of Mathematics then. There were 4 Professors, Hardy, Littlewood, Dirac, Eddington — what a great combination, with many distinguished staff members also. In older times in Cambridge, every one who entered the University first did the Maths Tripos Part I. Thereafter one either changed to other subjects like Theology, Medicine, Law, or continued with Maths. A certain element of this was still there in my Cambridge days. 'Those who continued on with the Maths did at the end of 3 years the Maths Tripos Part II a prestigious and most demanding examination. Till recent times most of the Maths staff in British Universities would be drawn from those who had done this course. The pass list was arranged in order of merit. The best group among them were called Wranglers. The one who came first was called Senior Wrangler. He was much honoured in British Educational life. At the graduation ceremonies of every year it was the Senior Wrangler who got his degree first. Incidentally the one who came last, but passed, got the Wooden Spoon in the same ceremony. There used to be quite keen competition for both top and bottom places. A few years before I got to Cambridge, the system of issuing the pass list in order of merit had ceased. There still continued an old custom where the results of this particular Tripos were read out by the Chairman of Examiners at the Senate House at a time and date prescribed by Statute. I recollect that during my year, I went along with other friends from Christs to "learn the worst" as we could say. A story is told of Lord Kelvin famous mathematician over 100 years ago. He was Thomson in his younger days. He loved sleeping in so instead of going to the Senate House himself he sent a College servant to find out the results. Thomson still in bed as the man returned asked him "Who came second ?". The memorable reply was "You Sir". To proceed with my story. It was by a chance circumstance that Professor Dirac agreed to supervise me for the Ph.D. He usually did not take on students. The Faculty Board had informed me 3 months earlier that they would let me know who my supervisor would be — and I had not heard, and the Academic Year was almost starting. Then one morning I had a letter from Professor Dirac in his very neat handwriting. It went something like this: As I am appointed your supervisor, you must come up and see me sometime. I lecture Tuesdays, Thursdays, Saturdays at 10. The best time to catch me is immediately after a lecture. I saw him at the earliest opportunity. That is how I got started. The succeeding years were great times. Concentrated delights, frustrations, foolishness, errors, lucky guesses or ideas that worked — all made up the Ph.D. years and later the Fellowship and lecturing years. Thoughts on Education After 45 years as an academic, I feel I could say something about the learning process, at any rate in the mathematical field. First, one has to have a passionate and desperate desire to understand something, to formulate a problem, narrow it down and concentrate upon it. Days, weeks, months, maybe, and result is often frustration and temporary abandonment. Then a period of incubation when the subconscious is at work. Then unexpectedly comes illumination. To take a homely example. I try to recall something and my memory does not oblige, however hard I try. Then some time later, perhaps the next day or so, I am not thinking of the matter at all, and the answer pops up. In scientific matters, those moments of illumination are the landmarks of discovery. The day Archimedes was at his bath, and ran through the streets of Syracuse, clad only in the rapture of a new discovery, should be celebrated as the first recorded version of a great moment of human emotion and illumination. It is said of Ramanujam that he would go to sleep thinking up some difficult problem, and the next morning he would wake up with a proposition in the theory of numbers or some long series expansion. When asked to explain how the proposition came to him, he would say that his Mother Goddess had explained it all to him in a dream. We may paraphrase and say that the subconscious was active during his sleep. In the fourth stage of the learning process, one recasts the results and systematises it. Thus, the four stages are : concentration, incubation, illumination and systematisation. Einstein was once asked whether his life had been of great thrills with all those discoveries. He said that when he was thinking and concentrating hard, it was pain and anguish. The pleasure came later after a new idea triggered, or when one realised the scope of what one had done. So education without the pain of concentration and effort is no education . at all. It is a fashionable trend nowadays for organised education to skip all the difficult things, and go through the motion with easy things. As parents we get concerned that whereas, education should be concerned with thought development, there is a temptation in schools to go in for thought elimination devices. Even in this age of gadgets and machines, the human being is the most intricate and exciting of all machines, and it has the further merit that it is about the only one that can be mass produced by unskilled labour with comparative little expense and so much more pleasure. Soon after the last War, the New Maths became the vogue, especially by the persuasion of American professors of mathematical education. They said it will bring mathematics within the reach of all — a most laudable objective. Over the years it has not quite turned out that way. In some countries, they have taken advantage of the language precisions of new maths to teach the contents of the old in -the new language. In some other countries the time for Mathematics has gradually dwindled and the contents have suffered. I often wake up with a bad dream —with the image of the grin of the Cheshire Cat. In the story, the grin remained, while the cat disappeared. My bad dream is about the New Maths where the newness like the grin remains, and the contents like the cat have gradually disappeared. I say it was a bad dream. I hope it has little relation to the facts. John Adams the historian has said : There are two educations. One teaches us how to live, the other how to make a living. We need to keep these perspectives in balance. Any thought on the future of universities ? First, about University Mathematics. I indicated before that Mathematics being an Abstract Art, there is the danger of it becoming isolated from the rest of Academia. In the 19th or early 20th centuries, mathematics made great impact on philosophy, science, education etc. Nowadays they are too isolated. There is the need for abstract mathematics, which is essential for long term perspectives. There is also the need to be in touch with the real world. These two aspects have to be kept in balance. While this is a matter of worldwide concern, I am confident that here at La Trobe the balance could be kept, and Mathematics will continue to prosper. It is very pleasing that University education is now available for so many more students than they were 45 years ago With expansion however came also some problems. I refer to one change that has come about in universities. When I joined the staff there were very few Ph.D's, but now that is the norm. This is a very good thing, since academics are able to continue research, despite the pressures of other duties, having benefited by the earlier period of intense research activity for the Ph.D. But this Ph.D. cult also encourages narrowness. Whereas a teacher of a subject should see it in its wholeness, the Ph.D. area often tends to take over. I believe that student needs and subject progress require from staff a balanced approach. I think also that while we love our special worlds and love the University world, we overlook that we are in the total world of life and living and cannot escape the demands, the joys and sorrows of the wider world. Universities were centres of great liberal human values, which spread to all corners of the world. Universities are homes-of Good Causes, even if lost causes. Our world can have in it so much sadness and savagery. 'Every man for himself" the elephant said, as he danced among the chickens. Many of us know of C.P. Snow and the Two Cultures. He was a fellow of the same College and so I knew him quite well. He died a couple of years ago. When I visited Cambridge soon after, I found that the Urn containing his ashes is kept on a pedestal on the edge of the old swimming pool at Christ, where there or four previous Urns from 2 to 300 years are also kept. A verse on the plinth attracted my attention. It may have been with C.P. Snow's approval or his wish. It is from a Jewish Father of 2000 years ago, Hellier the Elder. It goes: If I am not for myself, who am I ?
If I am for myself alone,
whoam ? If not now, wHen ?
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