This is a piece I wrote for the Alumni meet of Ph.D. students of the Department of Mathematics of IIT Guwahati to be held in Sept. 2020. More than looking back at my time at IITG from 1995 to 2003, I also reflect on the purpose of research and what I believe is important for research in mathematics in the future.
It is indeed a pleasure to be asked to write and to be able to send my good wishes to the on the occasion of the Alumni meet of Ph.D. students of IITG. I have been informed that to date 84 PhD students have graduated from the department, that the department currently has 79 research scholars, and that 20 new students are going to join this semester. These are very large numbers and a completely different scene from how things were when we started the Ph.D. programme in the department in 1996.
We were at Panbazar then, in the building of the Institution of Engineers under the Panbazar over bridge. We began in 1995 with only three engineering departments – Computer Science Engineering, Electronics and Communications Engineering and Mechanical Engineering, and the so-called ‘service’ departments -- Mathematics, Physics, Chemistry, and HSS, each having at most five or six faculty members. Student intake numbers for the B.Tech programmes were also very small then. The first batch of B. Tech students arrived in Guwahati almost before everyone else. The hostels were rented buildings in different parts of the city. The labs were not properly set up or equipped. There were not many faculty or staff. We were largely dependent on guest faculty from the nearby Cotton College and other city colleges at least for many of the courses in the basic science subjects. I was the first person to join the department in July 1995 (in fact, I was the fourth faculty to join in the whole Institute after the Director, Prof. Dhiren Buragohain, Prof. Gautam Barua and Prof. Devdas Kakati). Rafik, Sanyasiraju and Dalal joined soon after. Prof. P. Bhattacharyya (who passed away very recently) became our Head. Dr. S. Ponnusamy and Dr. B. Thatte also joined at around that time. Between us we started teaching the Maths courses for the B. Tech students.
But that was not enough for us. We were a young faculty and we were all very interested in continuing with our own individual research as well as establishing a tradition of quality research at IITG as soon as possible. I invited my D.Phil. supervisor from Oxford, Dr. Peter M Neumann, to come and get the ball rolling. He most kindly agreed to come in the summer of 1996. Wanting to make the best of this opportunity, and understanding that a couple of standalone lectures in algebra by my supervisor would not really work unless we did some preparatory work, we decided to expand the whole concept into a full-fledged 8-week long lecture series on permutation groups and open it up to anyone (with a graduate degree in Mathematics) who wanted to join. Two other mathematician friends, Dr. H.D. Macpherson from Leeds, UK and Dr. R. G. Moeller from Iceland also agreed to speak at the lecture series. About 60 participants attended the course that was supported by the NBHM, and the 16 lectures delivered during the course became the sixteen chapters of a monograph that was later published on the subject. That course was a huge success and it was a great way to get the research activities of our department started.
Two of the three note-takers for the course – Shreemayee Bora and Shabeena Ahmed -- went on to become the first Ph.D. students of the department, Shreemayee under Rafik and Shabeena with me. Jiten Kalita also started at around the same time with Dalal. Today both Shreemayee and Jiten are faculty at IITG. And the third note-taker for our course – Dr. Bhaba Kr. Sarma – is now a senior professor at IITG. In that sense, the impact of that one course can be felt in the department even today. All three of our first batch of Ph.D. students were awarded their degrees in 2002.
We also wanted to have our own Maths masters programme but we were not sure if a regular Maths M.Sc. would be the right thing to start since one could get that degree from any of the universities in the region. We wanted to come up with a different course. The CSE department was our closest partner department – and we broached the idea of starting a two year M.Sc. programme in Maths and Computing, with their help in the year 2000. Over time, that programme proved to be a great success, so much so that later a full-fledged 4–year B.Tech. programme in Maths and Computing was started by the department.
I left the department in the summer of 2003, soon after organizing, with the help of my colleagues in the department, a 2-week workshop (with about fifty attendees) followed by a one-weeklong conference on Geometric Group Theory in December 2002. The conference attracted more than thirty reputed mathematicians from India and abroad and helped to put IITG on the research map of mathematics worldwide. Many other events have happened since and the faculty of the Mathematics Department of IITG have been very successful in maintaining a high standard of teaching even while carrying on with high quality research. Looking back on how the department has shaped up in the last years, I have ample reason to be proud and happy and I congratulate each and every one of you for contributing to that development.
Before I end, I would also like to say a few words about what I believe I have understood about the world of research, especially in mathematics. I can’t claim any authority on the subject because I wasn’t a very successful researcher myself but I can at least tell you why I failed. Somehow I was just too matter-of-fact, too rational, too little of a dreamer, so while I enjoyed the research I did, I somehow felt I was not creative enough. I was happy when I produced a nice result, but I didn’t dance around in joy. Once when I waited for a full week before telling my supervisor about having solved a problem that had been bothering us for months, he shook his head gravely and said, ‘Wish you would show a little more excitement, a little more passion.’ That is the point I am trying to make. Research is such a thing that if you simply do it well, it is not good enough. You have to live it, love it, breathe it, think about it all the time, discuss it with others who are also working on similar things, and really feel that proving the next theorem is a question of life and death for you – in other words, you have to live your research passionately. If you cannot do that, then perhaps you should be doing something else. Because research is one of the few things where quality is all and quantity is almost irrelevant (at least in ideal circumstances). If you are disciplined and keep working at your subject every day, you will keep producing results which will give you new research papers and take you places, but if the spark is missing, then these papers will be not good for much else besides elongating your own CV and getting you a promotion or a better job. It will not change anything in the world, it will not help you to understand the world better.
But true research is supposed to do just that – help you to understand the world better. So you have to have the courage to ask the right questions, the interesting questions, even if they are difficult. There are some questions which are doable, but they are often less interesting, and less meaningful. If you want to be a true researcher, and not just a successful one, then you have to not be afraid of asking the difficult questions and spending all the time it takes looking for an answer. I know that doing this is neither feasible nor advisable if you are a Ph.D. student with a scholarship that is running out or even a faculty who wants to get a promotion or who wants to write a paper to present at the next prestigious conference in your subject area. That is precisely where the contradiction lies – that our system forces us to compromise and be happy with our mediocrity even while demanding that we do our very best, and live up to the highest ideals of our profession as teachers and researchers. That is probably the reason why I left mathematics – because I could see that I could only do so much, but the demands of true research and my own expectations from myself as a researcher were much higher. I knew I could not be happy hiding behind a lie and pretending that all was well. That is why I left.
So much for individual research; next, a word about the topics of research. Today after at least a century and a half since the establishment of the standards and methods of scientific research and enquiry, most of the easy questions in every line of enquiry have more or less been answered. The questions left are the big ones and the suspicion is that these questions are still unanswered simply because the tools we have in our hands might not be enough to solve them. Hence now the time has come when every researcher must get out of their comfort zones, and learn how to use a new set of tools, or learn to collaborate with a new set of people who uses other tools, in order to find answers to the BIG questions that are still left unresolved. This means increased collaboration and cooperation and moving into new hybrid forms of research that do not resemble what we have learnt or seen so far. This also means that we have to learn to work in groups, where problems are sought to be solved by putting all heads together.
This also means that gone are the days when mathematicians could afford to sit in their own offices and pursue their own private research fantasies. One can still do that, if one believes that doing research is an end in itself and needs no further justification, or if one is happy to keep churning out routine, technically correct but physically irrelevant stuff that will not make any difference to knowledge. But if one wants to achieve more, then the way to go looks somewhat different. The future of basic science research lies in developing centres of expertise – with a group of researchers working on one big question gravitating to one institute, those working on another big question to another. It also means rigorous and hard years of apprenticeship for each of these researchers, before they have mastered their many tool boxes. Translated into our present system it means a long period of apprenticeship at the post-doc level after finishing one’s own Ph.D. where one learns to use other tool boxes from other experts; it also means spending several years in equipping oneself before moving to the stage of becoming a Ph.D. supervisor. It also means total commitment to the subject and a supportive system that understands the demands of real hard core basic research and allocates time and resources for it. And above all it means researchers who are ready to go the whole hog regardless of how hard the going is, who do not care what else they get by doing research as long they get a kick out of what they are doing, who will start dancing with joy when finally the ‘eureka’ moment comes.
I cannot end before making a case for three important and vital areas of research which seem to have been neglected so far at IITG – research in mathematics education, research in the philosophy of mathematics, and research in the history of mathematics, and more generally, its place in the history of science. These are not soft subjects, make no mistake. Research in these areas are as difficult as doing mathematical modeling or fluid dynamics. But research in these areas are important if we want to see the link between our research and our humanity, between mathematics and the liberal arts, and also to bring about changes in how mathematics is taught in the classrooms. Research in these topics will certainly help us to understand the world better – and perhaps also to make it a better place for all of us. It will be a dream come true if these subjects also became topics of serious research at IITG in the future.
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