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Mentoring Mathematics Research

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Summary

I abhor the practice in which a guide is assigned to a student immediately on entering the graduate school and the guide looses no time in proposing a problem – something that unfortunately happens all too often in our universities.

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According to an internet dictionary the word ‘mentor’ means “an experienced and trusted adviser”. The word comes from Greek mythology – Mentor was the teacher of Telemachus, son of Ulysses in Homer’s Odyssey. When I began mentoring mathematics students some 55 years ago, I did not quite fit that description – I was not experienced. I had not yet got my PhD (but had published 3 well received papers). And my lack of experience showed – the first student I mentored quit mathematics without a degree. This student did a piece of research which he showed to me and I discouraged him from trying to publish it. I had a high opinion of him and thought what he had done was routine and that he should aim higher. Some 6 months later we found that a student of Atiyah – a big name in mathematics – published the same piece of research in a respectable journal. What is more, unlike my student, he had been asked to look at the problem by his mentor. My student came up to me and said “It wasn’t that bad, was it boss?”. I felt pretty awful. This episode is something that I am unable to live down to-date.

 

There were other students who did not make it to a PhD, but I do not hold myself primarily responsible for that as I do in this case. My relationship with that student or that of any other student has been largely informal though in recent years the age-gap has made it practically impossible. I used to insist that my students address me by name and without the prefix ‘Professor’ but do not do it any longer.

 

Till some five years ago my interactions with young people was limited to graduate students and junior faculty. I have been by and large a “successful” mentor: quite a few of my students and junior colleagues are established mathematicians of high standing. But I am not sure how much credit I can claim for that. There is an old quote of Francis Bacon which is along the following lines: It is a pity that those whom we would like to teach most are the ones who need it least. Most of my students belonged to that category and so would have achieved the heights they have scaled without my interference – the branch of mathematics they pursued would perhaps have been different. The standard practice in most graduate schools is for the guide to propose a problem for the student to pursue. I did do this in some cases but often enough, the student found the problem to work on by himself, though I had an indirect role in that I educated him in relevant topics. I think that is the ideal thing to happen if the student is highly talented. Less talented ones may need some help in finding a problem to work on. The mentor with experience behind him can locate problems which are interesting yet accessible to a student with somewhat limited knowledge. Basically no two students are alike and one needs to channel each student in a way suited to his/her tastes and abilities. Most of my students moved away from my own area of specialisation in which they wrote the thesis and I was happy when they did so. I have always insisted on my students acquiring a wide scholarship: for one thing that will help them branch off into areas other than the area of the PhD thesis; secondly even if one is a successful researcher it is not clear that your work will stand the test of time while if you acquire wide scholarship you can certainly pass on to the next generation something that has lasting value.

 

I abhor the practice in which a guide is assigned to a student immediately on entering the graduate school and the guide looses no time in proposing a problem – something that unfortunately happens all too often in our universities. I was an ardent admirer of the Soviet system before the break-up. In the fifties and sixties they produced a galaxy of great young mathematicians. That seemed the result of early spotting of talent and subsequent nurture. However, as an expatriate Russian mathematician told me that while the system took care of enormously talented youngsters, it simply was not good enough to take care of others who were in the second rung of the ladder whereas the American system made good mathematicians out of lesser talent.  I realized at that point that I was extremely lucky in that at TIFR. The students were a highly talented lot. But even among them, as I said earlier, there were some whom I could not lead on to a degree. But I do not have serious feelings of guilt as with the first student I mentioned: they were unable to cope with the peer pressure that they felt. In two of those cases they were not making adequate progress on the problem I had suggested, and I hinted at how they could proceed thinking that I was helping them. As it turned out they were upset with me –  they perceived it as not allowing them to think more for themselves!

 

I have essentially spoken of my experience as a mentor and I leave it to the reader to draw conclusions about mentoring from that. I think I owe my ‘success’ largely to the student recruitment methods at TIFR and of course the inevitable luck.

 

M S Raghunathan is a mathematician with Centre for Excellence in Basic Sciences, Mumbai. He is a recipient of the Padma Bhushan honour. Views expressed are personal and do not necessarily reflect those of Confluence, its editorial board or the Academy.

This article is part of a Confluence series called “Mentor-Mentee Relationships in Academia: Nature, Problems and Solutions”

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