I thank the editors of Confluence for inviting me to share my “perspective and thoughts on the process of mentoring in the broad area of mathematical sciences”. There are many outstanding mathematicians in India who are undoubtedly better qualified to speak on such an important topic. Some of them have even taken effective steps to improve mathematics in India considerably.

I believe that it is important to start from an early stage and spot talented students in mathematics as early as possible. This is essential for mathematics to blossom fully in India.

My journey in mathematics essentially began in 1971 when I joined ISI as an M. Stat. student. For the first time I was being taught by active mathematicians and statisticians who completely changed my outlook and approach to mathematics. At that time overall scenario of mathematics in India was not very satisfactory. There were essentially two internationally recognized centres in the country for research in mathematical sciences – TIFR and ISI (located only at Calcutta then).

TIFR became a strong centre for research in certain central areas of mathematics such as number theory, algebra, algebraic geometry, Lie groups, representation theory, ergodic theory and other specialized fields. Many TIFR mathematicians became leading figures in the world in their respective areas of research. ISI was considered as a leading centre for research in statistics and probability in the world. It was probably the most prominent good centre for research in certain areas of mathematics too.

However, these two institutes stood as isolated ivory towers with hardly any impact on the rest of the country. There was practically no interaction between even these two institutes. One can see how bad the situation was from the fact that for quite sometime the Bachelors and Masters programmes in statistics of ISI was possibly the only high class option available to most students in India (especially in the eastern region) who wanted to pursue higher studies in mathematics. As late as in 1979-80, Armand Borel, a permanent professor of mathematics at the Institute for Advanced Study, Princeton, expressed his disappointment to me that TIFR, in spite of having so many world class mathematicians, had no impact on the country.

Since then India has come a long way in mathematics. Now there are many good options to study mathematics available to students. Formation of the National Board for Higher Mathematics in India (NBHM) by DAE sometime in the late 70s was a turning point for higher mathematics in India. NBHM regularly organizes schools in mathematics for college and university students as well as for research fellows and young faculty. It also conducts Mathematics Olympiad for school students. Led by some of the best mathematicians of the country and with active participation of mathematicians from across the country, by now it has made invaluable contributions to the improvement of mathematics in India. Added to this the introduction of B. Math.-M. Math. program of ISI, the Mathematics program of CMI and IISc., and introduction of mathematics in new IITs, IISERs, NISERs etc. have helped the growth of mathematics substantially in India. Today India is internationally recognized as one of the advanced countries in mathematics.

In spite of all these, there is still much room for improvement. I will now proceed to give my ideas on how we should go about making further improvement. There are several stages of education starting from school to college to university and finally to research that a person has to pass through to become a scientist. I shall be concentrating on each of these stages separately.

School Level

I shall repeat a view which has been expressed at various fora. At the beginning level, say up to class four or five, the course content should be minimal. Till this time the conventional classroom teaching should be limited to languages, literature and arithmetic only. This will leave time for extra curricular activities like sports, debate, drama, music, reading stories and articles, fun games using geometrical shapes, numbers and natural sciences etc. Visits to museums and science museums should be organized. Written examinations should be conducted on languages, literature and arithmetic only.

All major educational centres should have outreach programmes to schools. In this respect, the introduction of mathematical olympiads for school students at higher level by NBHM has been very effective in generating interest in mathematics. This has given opportunities to the students to attack problems beyond their school curriculum and think originally.

College and University Level

In my opinion, this is where independent India went quite wrong. To start with the salary of teachers as well as funding for research were quite poor. The infrastructure of universities and colleges were dismal. This automatically led to serious brain drain problem. The importance of bright young students being taught by active scientists was not realised even by scientists themselves. I have often wondered why did planners of independent India not try to strengthen the universities. Did J. C. Bose, P. C. Ray, K. S. Krishnan, S. N. Bose, M. N. Saha, Vijayraghavan, R. C. Bose and even P. C. Mahalanobis etc not teach in universities and colleges?

ISI was the first research institute in India that introduced Bachelors and Masters programmes in statistics. The high national and international standing of ISI’s B.Stat. and M.Stat. degrees is a testimony to the difference that learning from high quality researchers can make for young students. In a KVPY interview a professor from IISc told me that they were finding it hard to get properly trained and motivated research scholars because of the poor teaching in universities and colleges. Through KVPY programme they hoped to catch some bright students immediately after they left school and train them during vacations at IISc and other institutes. Other programmes where some limited number of bright students were given opportunities to work with active mathematicians and scientists during their vacations were also introduced. Clearly these measures were too little for a vast country like ours.

NBHM has done a splendid job by organizing regular training schools for college and university students, research scholars and junior faculty. It also organizes schools in some specialized topics. Since last one and half decades several new IITs, NITs, IISERs, NISERs have been opened. All of them are required to run UG and PG programmes. This has helped to improve mathematics in India and is quite likely to show its benefit to the country in the near future. However, it is unlikely to cater to the majority of students. The standard and the infrastructure of the universities must be improved substantially if India wants itself to be counted among the best in the world.

Research in Mathematics

It has been correctly said by Professor R. Gadagkar: “A Ph.D. degree is awarded to a person who has shown evidence of conducting original research and has produced significant new knowledge to a chosen area of work.” (source article) However, in my opinion if the thesis contains a new and interesting idea or a new way of looking at a known thing, it should also be enough. To achieve this the supervisor of a research fellow should leave him/her as free as possible. However, it is the responsibility of the department to which the research fellow belongs to prepare her/him to a level where he/she is in a position to identify which area interests him/her the most and choose the supervisor accordingly. In mathematics, except in highly exceptional cases, a fellow must not be assigned a supervisor in the first year of her/his joining the department. During this period the student should be exposed to the basics of several current areas of research.

It is the responsibility of the research fellow to prove herself/himself worthy of a Ph.D. degree. The supervisor should be careful not to contribute much to the work of a research fellow though he or she may help the fellow to find suitable problems. He or she may also suggest some directions in which to proceed if the fellow seeks advice.

Academic Autonomy

As a precondition to approving grants and recognizing the programmes, the regulatory bodies should not insist on universities and institutes following the course structures laid by them. It is completely justified for the regulatory bodies to satisfy themselves that the programmes of educational organizations meet the desired standards before recognizing the degrees and granting funds. The ideal structure varies from subject to subject and also depends on the strength of the organization. The regulatory bodies can lay down some guidelines and specify minimum standards to be followed to get their recognition. This will allow many educational organizations to impart education of the high standard that they are capable of.

There is a tendency among the planners now to impose teaching on all research institutes. This cannot be done overnight. The research institutes have not been developed like universities. Many of them do not have proper classrooms. Most of them are small with a small number of scientists working in a few specialised areas. The infrastructure of all research institutes should be strengthened, both physically as well as human resources, before insisting that they run full UG and PG programmes in science. It will do great harm to the country if our scientists are not given sufficient time for their research.

Finally, I must point out that science in general and mathematics in particular is for creative thinkers. One must give total freedom to researchers to choose his or her area of research. Science, including mathematics, has always produced and will continue to produce useful work if the creative thinkers are given complete freedom.

S. M. Srivastava is Visiting Professor at Indian Association for the Cultivation of Science, Kolkata. Views expressed are personal and do not necessarily reflect those of Confluence, its editorial board or the Academy.