Sunday, January 13, 2008

India in world mathematics -M.S. RAGHUNATHAN

“The intellectual potentialities of the Indian nation are unlimited and not many years would perhaps be needed before India can take a worthy place in world mathematics.Those are the words of A. Weil, one of the greatest mathematicians of the 20th century, written in 1936. Weil was not a man to be easily impressed; and his assessment of our capabilities were based not just on our record in ancient and medieval history and the achievements of the towering figure of Srinivasa Ramanujan but took into account contemporary Indian perfomance. Colonial rule was not the ideal environment for that favourable prognosis to be realised; yet we made some modest progress.At the dawn of freedom there were in the country a dozen or so mathematicians of high calibre still active. And fully realising our potential was surely a tiny part of our pledge in our “tryst with destiny.”On the eve of Independence there was notable mathematical research activity in some of our university departments; those of Allahabad, Calcutta and Madras were in the lead, work emerging from these centres receiving some international acclaim. The Indian Statistical Institute (ISI) in Calcutta had acquired a big reputation in Statistics.
During the first decade after Independence, even as these institutions continued with their good work, a new arrival on the scene, the Tata Institute of Fundamental Research (TIFR) was making impressive progress.The 1960s saw the coming of age of Indian mathematics. India has since made some very substantial contributions to mathematics. People working in the country have made fundamental contributions to certain areas of mathematics, notably Algebra, Algebraic Geometry, Lie Theory, Number Theory, Probability Theory and Statistics — contributions that are milestones in these subjects. There have been interesting contributions to other areas too, but their impact has not been as impressive.A major mathematical event, the International Congress of Mathematicians (ICM), has been taking place once every four years since 1900 (with breaks during the World War years) with ever increasing international participation. The meet is built around prestigious invited lectures numbering about 200: some 20 “plenary” one-hour lectures are meant for the general mathematical audience and are given by eminent figures who have had a big influence on the evolution of different mathematical areas. The remaining, more specialised, talks of 50 minutes duration are given by other outstanding contributors to diverse fields in mathematics. (The numbers mentioned are those in recent congresses; they were much smaller earlier on.) It is at these Congresses that the Fields Medal, the most prestigious international award for mathematics, is given.Some idea of the Indian impact on the world of mathematics may be gleaned from the fact that since 1954, in every Congress except in 1966 and 1986 there has been at least one invited talk by an Indian working in India; and all these talks have been in areas mentioned above. There have been two plenary talks by Indians but both were by non-residents. However, on the whole there have been far fewer talks by non-resident Indians than by those working in India.The Fields Medal, by far the most prestigious award for mathematical achievement, is awarded at the International Congresses. This prize has so far eluded India but there are instances of people coming close to it. (The medal is awarded only to mathematicians under 40 and its monetary value is a pittance in comparison with the Nobel prize). Several Indian mathematicians have, however, received the Third World Academy Mathematics Prize (awarded every year since 1980), an award for excellence in mathematical research in the developing countries. M.S. Narasimhan (who retired from the TIFR in 1992) received the King Faisal Prize for Mathematics in 2006. This is an international prize given for outstanding work in the different sciences, and mathematics gets its turn once in four years. All the recipients before Dr. Narasimhan were Westerners. Also in 2006, C.S. Seshadri, who is Director, Chennai Mathematics Institute, was awrded the ICTP Prize for mathematics, yet another prestigious award for scientists from the Third World. The same year, Manindra Agarwal of the Indian Institute of Technology and two of his erstwhile students, Neeraj Kayal and Nitin Saxena, bagged the Godel Prize for outstanding work in Theoretical Computer Science (done in 2002). A (woman) mathematician, R. Sujatha of the TIFR, was awarded (again in 2006) another international prize meant for mathematical achievements in the Third World, the Ramanuajan Prize instituted jointly by the International Centre for Theoretical Physics and the Niels Henrik Abel Memorial Fund. The Abel Memorial Fund also
provides funds for the Abel Prize which rewards mathematical achievement on a scale similar to that of the Nobel. This year’s prize went to S.R.S. Varadhan, of Indian origin. Dr. Varadhan’s formative years were spent atthe Indian Statistical Institute in Calcutta. Another indication of the high levels achieved by Indian mathematics is that three Indian mathematicians working in India have been elected Fellows of the Royal Society of London. Two non-residents (Dr. Varadhan and Dr. Harish-Chandra) and Srinivasa Ramnaujan are the only other Indian mathematicians who have been conferred this privilege.The last two paragraphs briefly outlined the high points of Indian achievement in mathematics. These peaks, however, do not by any means tell the whole story: except the Godel Prize, all the other achievements came from the TIFR and the ISI. In fact, the TIFR accounts for by far the larger share. The general level of mathematics outside a handful of institutions of higher learning leaves much to be desired. One finds at most university departments neither good quality research nor superior scholarship.The present situation is indeed depressing; and in many ways things are on a further decline. There has been a steady loss of interest in the pursuit of mathematics (in fact of all the basic sciences) among the young over the last three decades. This is largely due to socio-economic factors. Till recently, career options for mathematics graduates was essentially limited to the academic profession. The academic profession is of course not attractive in terms of emoluments: a fresh management graduate enters his or her career at a salary which is often higher than what the academic retires on.Unattractive economic status is of course nothing new to the academic profession, but it no longer commands the respect it used to in an earlier era. ”Midnight’s Children” seem to have had a definite advantage over their children in the matter of the quality of their teachers.
Despite all this, some talented youngsters will still pursue mathematics, but most of them seek to do it in Europe or the United States. One reason is that the academic in the West has a much better socio-economic standing; a second reason is the sorry state of most of our institutions of higher learning — an eager student cannot get exposure to truly exciting mathematics except in a handful of places. And even these, while being good, are no match for a Harvard or a Princeton. On top of that, many Western universities are actively canvassing to get Indian students enrolled in their graduate schools.Higher education in the country has come to mean, especially in the context of economic liberalisation, education that leads to big emoluments. The policies of the state are in tune with this perception. Most of the state support for higher education is de facto a subsidy for producing (managerial) human resources for business and industry. Scant attention is paid to promoting learning for its own sake: higher studies that do not cater to commerce get short shrift.For example, State governments have not allowed universities to fill sanctioned positions in their science or humanities departments, by withholding the needed financial support.Mathematics has always played an important role in diverse human endeavours. Physics has had over the centuries a symbiotic relationship with mathematics; so also technology, especially since the Industrial Revolution. Biology and medicine, as also the social sciences, which were relatively impervious to advanced mathematics till a hundred years ago, are now benefiting immensely from highly sophisticated mathematical intervention. In the last few decades the world of finance has turned to higher mathematics for help: Wall Street employs mathematics Ph.Ds routinely.In such a context, it is important that we make an all-out effort to improve the state of mathematics in the country. And any improvement of the general scenario is possible only if we have good mathematics teachers at all levels. And to secure that, it is imperative that the teaching profession be made socio-economically attractive.In sum, the mathematical scene is a mixed bag. We have, on the one hand, an impressive record on the frontiers of mathematics even as the standards in the mathematical community at large are far from satisfactory: we are yet to claim our “worthy place in world mathematics.There is, however, room for some cautious optimism about the future. The Tata Institute of Fundamental Research, which accounts for most of our peak achievements, continues to perform at a superior level; that institute has set up a centre in Bangalore where areas like Differential Equations are pursued with vigour. The Indian Statistical Institute has established branches in Delhi and Bangalore; these, along with the headquarters in Kolkata, are lively centres producing excellent work.The government has set up two research institutions along the lines of the TIFR, one in Chennai and one in Allahabad, both of which are contributing to enhancing the quality of our mathematics. The Indian Institute of Science has in recent years assembled an excellent, youthful faculty in mathematics, making its future very promising. The IITs are making serious efforts to raise the standards of research and scholarship in mathematics.Some university departments are also trying to do this, but their meagre financial resources make the task very difficult.In the recent past there have been two initiatives at providing excellent undergraduate education in mathematics. One was the creation of the Chennai Mathematics Institute where undergraduate students are taught by active, front-ranking researchers. The Indian Statistical Institute in Bangalore is running such a teaching programme. Both institutions have met with considerable success in producing scholars well poised to embark on a career in mathematics. In the last couple of years the government has set up two “Indian Institutes of Science Education and Research” with the same aims and one hopes that these efforts will also succeed.On the whole, our nurture of the potential has been less than satisfactory. We need to make greater efforts in that direction. The diamond jubilee of India’s Independence is a good occasion to reiterate the resolve to do that.

M.S. Raghunathan, a Fellow of the Royal Society, is DAE Homi Bhabha Professor. He was formerly Professor of Eminence, TIFR. from-HINDU

1 comment:

Arvind said...

A very welcome chance reading of the article.Being a retired unaffiliated mathematics researcher and teacher, I find this space specially valuable for keeping in touch with a dear area.Thanks.Shall continue to look into this space.