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Bill Gates and Michael Dertouzos
1 Extracts from 'Professor Calculus'; article on Professor M C Chaki ;appearing in 'Midweek' of The Statesman, dated Wednesday, October 28, 1998; page 4.
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1. Extracts from 'Professor Calculus'; article on Professor M C Chaki ;appearing in 'Midweek' of The Statesman, dated Wednesday, October 28, 1998; page 4.
He lives, breathes and dreams of revamping the study of mathematics in school and college. His contribution in the field of general relativity has given tremendous impetus to research scholars abroad. He retired as Sir Asutosh Birth Centenary Professor of Higher Mathematics in 1978.
Priyanka Mazumdar in conversation with Professor M C Chaki
Room No 21, Hotel Savoy, 27 Sashibhusan Dey Street, Calcutta. This has been the permanent address of the seniormost mathematician of india for the past 52 years. Numerous boarders have come and gone, the hotel itself has witnessed a change of ownership, yet for Professor M C Chaki, Room No. 21 has been home in the city.

Walking down from Bowbazaar, you might take a while to locate the hotel. A small doorway leading to a narrow corridor brings one to the reception. A flight of stairs leads up to Room No 21. Open the door and you'll see, breathe and feel mathematics. There's not a nook or corner which isn't stacked with books. In fact, they are even piled on the bed. At night, the bedcover is removed along with the books and placed elsewhere. In the morning, the books are heaped back again on the the bed.

Born in 1913, the 86 year old mathematician is a living example of how a student can be influenced by his mentor in developing a love for mathematics. In his childhood, Prof Chaki was not fond of mathematics. He was drawn to literature, painting, music and other fine arts.  "Maths class was very boring," he says. It was in Class IX that he began to appreciate the beauty of the subject. He still fondly remembers his teacher, Durgadas Banerjee, at Gaibanda High School, now in Bangladesh.

After passing Interscience from Bangabasi College, Chaki chose mathematics and Sanskrit as an undergraduate. Sanskrit is still his second favourite. After completing his MA in Pure Mathematics, he taught for five or six years at Bogra College in Bangladesh, Subsequently, he settled in Calcutta and taught at Bangabasi College. From 1952 onwards, he joined the Department of Pure Mathematics, Calcutta University. He retired as Sir Asutosh Birth Centenary Professor of Higher Mathematics in 1978.

But Prof Chaki's career did not end with his retirement. Even at the age of 86, he supervises the work of six research scholars. His papers on "non-symmetric harmonic space", conformally symmetric spaces" and "pseudo symmetric manifolds" have been much appreciated by the Polish and Japanese schools of differential geometry. Incidentally, his contribution in the field of general relativity, especially the concept of "Chaki (PS)" or "Chaki manifold" has given  tremendous impetus to research scholars in USA, UK, Canada, Russia, Belgium, Hungary and Yugoslavia. The Tensor Society of Japan has chosen him as the President of their international conference to be held later this year.

Though his works have  found international acclaim, Prof Chaki has never felt the urge to go abroad, even when he was selected Fellow of the Royal Astronomical Society of London in 1957 and is involved in the review and editing of many international journals. On several occasions, he has learnt languages either with the assistance of his friends or even independently, so as to continue  with his research work. He is very conversant in German, French, Italian, Russian and Persian, has a prodigious memory and has never carried any notes to class.

This "photographic memory" is also an index of his interest in the welfare of his students. He has devoted his entire life to encouraging and nurturing their potential and they in turn have relentlessly tried to fulfill his dream of establishing an institute. The inauguration of the MC Chaki Institute of Mathematics and Mathematical Sciences was a first in many ways. Prof Chaki had the privilege of witnessing the founding of an institute after his own name.

Aided by his 50-year-old faithful attendant, Prof Chaki endeavors to widen the scope of mathematical research from his quaint haunt. What follows are extracts of an interview:

Q. In your opinion, how can one develop an interest in mathematics?
Prof Chaki: Teachers play a vital role in inculcating and nurturing an interest in mathematics. Mathematics should be introduced to students in the form of short stories. There should be a genre of popular literature on mathematics.

Q. A logical approach is fundamental for students of mathematics. Do you agree?
Prof Chaki: Certainly a logical approach is very essential. In fact there should be a transition from intuition to logic. Even the figures used for demonstration should correspond to the logic used in the proposition.

Q. Could you be more specific on the use of figures?
Prof Chaki: While defining a triangle, teachers often use incorrect figural representations to explain their arguments. In most cases, the base of a prism is smeared with ink, imprinted and referred to as a triangle. But this figural representation does not correspond to to the logical definition of a triangle. On the contrary, the impression of just the outline of the base of the prism should be used. The visual and logical faculty should always be called upon synchronously in demonstrations.

Q. Are you satisfied with the manner in which mathematics is taught nowadays?
Prof Chaki: It is very unfortunate that adequate methods and proper techniques are no longer used while teaching. In fact, innovativeness is totally discouraged. Often cold water is poured on the fire of inquisitiveness. At present, undergraduate and postgraduate students have become only passive listeners. Inn most cases, students take class notes mechanically. Teachers do not entertain questions in class and often rebuke students for interrupting lectures. Teachers should clarify doubts and take interactive classes. Often students ask historical and etymological questions. There are many terms used in mathematics, the source of whose nomenclature is unknown. Teachers should try to give etymologically correct explanations for such nomenclature. Such information motivates students.

Teaching geometry in class, teachers often use faulty definitions based simply on figures. While defining the inside point of a circle, teachers often take the help of figures. But visual validity is not always logical validity. The best approach would be to say that if the distance of the point from the center is smaller than the radius of the circle, then the point is located inside it. Teachers should be careful with definitions and precisely enunciate [them].

Q. Have you thought of offering suggestions on revamping the study of mathematics?
Prof Chaki: I have been very disturbed by the way teachers go about teaching maths in school. For instance, the manner of introduction to "complex numbers" is very misleading. In fact, I have a manuscript ready on a special course for school mathematics. But publishers fear that both students and as well as teachers will not be ready to experiment with my suggestions. So they are reluctant to publish it. But the silver lining is that a research scholar of mine is doing his thesis on "pedagogic mathematics".

Q. A thesis on the science of teaching mathematics is quite unconventional ...
Prof Chaki: Yes. Actually research scholars usually choose topics from their special area of study at the postgraduate level. The fact that the foundation of higher mathematics is actually built in high school bothers no one. In order to do proper justice, the proposed thesis is a sort of critical review of the present-day studies of mathematics undertaken in different universities and colleges with reference to the higher secondary syllabus.

Q. What is your opinion of the maths syllabus at the undergraduate and postgraduate level?
Prof Chaki: Mathematics should be a coordinated program form the primary to the postgraduate level. But the syllabus has become an uncoordinated medley. There is a big jump from the secondary to the higher secondary level. As for the UG level, many new topics should be introduced. When I was the Chairman of the Board of Undergraduate Studies of Calcutta University, I had introduced Tensor Calculus. New topics should be judiciously introduced without making the syllabus unnecessarily heavy. The history of mathematics should be incorporated both at the UG and PG level. Maths, after all, is a cultural phenomenon, a mode of thought.

Q. A word of advice for students?
Prof Chaki: I would advise students to concentrate on their studies. For students of pure mathematics, deductions should be logical and the conceptual approach should be emphasized. For students of Applied Mathematics, the emphasis would shift to the perceptual side, taking into account sense perception.

Q. What's mathematics today?
Prof Chaki: Both pure and applied maths are becoming highly popular. Mathematics and Physics should be treated as allied subjects. Pure maths now aids in research work in molecular biology, anthropology, geology, hard-core computer engineering. In my opinion, differential geometry, topology, information science and probability theory are prospective branches of maths for the 21st century.

DISCUSSIONS:
Comment # 1: Received from
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