One Hundred Tamils
of the 20th Century
Mamanithar C.Jeyaratnam Eliezer
Prof C.J.Eliezer was honoured by the Federal Government
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
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
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.
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.
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
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
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
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
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 ?