A few years ago, I may have achieved a world record of sorts. 60 percent of the students in an advanced course that I was teaching requested me to become their PhD advisor.
To put the numbers in perspective, the class just had 5 students. I was flattered and agreed to supervise all the 3 students who made the request. Two of these students continued working with me, and one later moved to the research group of my colleague, Soumen Maity. This month, both my students have successfully defended their thesis. Jewel Mahajan defended on the 1st of December, and I am posting this blog right after the conclusion of Jishu Das's defence. Jishu has been co-supervised along with my colleague, Baskar Balasubramanyam. So, as of today, I am a proud advisor of 4 PhD students. May I exult in the joy for a few seconds and remind myself that in my field and at my career stage, this is a number to be reasonably proud of?
My first two PhD students, Sudhir Pujahari and Neha Prabhu graduated in 2016 and 2017 respectively; they both hold faculty positions now, and are doing very well. Sudhir joined as a PhD student at IISER Kolkata, and later moved to IISER Pune with me; Neha joined me at Pune. Incidentally, Sudhir is the second Math PhD from IISER Pune. The first PhD from our department is Yasmeen Akhtar, who was supervised by Soumen Maity, and is now a faculty member at BITS Goa.
As the year comes to an end, it feels great to reflect on my journey and experiences as a PhD advisor. The relationship between a PhD supervisor and students is one of the most important relationships in the academic journey, and also a fundamental component of how knowledge grows in a field. Several comparisons are made with other formative relationships in life, such as the parent-child relationship.
My relationship with each of my students is unique. While I saw (and continue to see) each of them grow as mathematicians and human beings, it is equally true that they have seen me grow as well, both professionally and personally. My students found me at distinct stages; the person who advised Sudhir and Neha (Students 1 and 2) was very different from the person who advised Jewel and Jishu (Students 3 and 4).
When Sudhir started working with me, I was six months into my first faculty position. Neha joined me a year or so after I moved to Pune. So, I was at an "early-career" stage when both of them started working with me. My early career years had their own set of struggles and anxieties. The key struggle was that I was experimenting with different ideas, and it took me some time to build a vision for my core research programme. I have written about this struggle here. In that sense, both Neha and Sudhir were fellow-adventurers, but the anxious part of me did indeed wonder once in a while if I had started supervising students too early on. Looking back today, these fears now appear unfounded. In fact, the success of a joint project with Neha helped us both to forge research paths to move ahead.
By the time Jewel and Jishu started working with me, I had passed through the "early-career" stage. I had clear research goals in mind, and was determined to pursue them systematically and in a focused way for the next few years. That is why, even as the pandemic raged and I was only able to meet my students online, I never had any doubt that both will finish successfully. In the case of Jishu, Baskar and I were co-advisors, and Baskar is a walking encyclopaedia on the topic. On their part, despite the difficulties of pandemic-induced isolation, both the students displayed a remarkable amount of resourcefulness and sincerity. We got used to discussing ideas and questions over long emails (and occasionally, long WhatsApp and text messages as well, a practice that I now strongly discourage in my students; WhatsApp and text messages are best used only for urgent communication). They took full advantage of several international conferences and seminars being held online, notwithstanding the late night hours in Indian Standard Time. Like any research project, our projects also experienced some turbulence from time to time, but it only made us more determined and excited to finish them. My work with Jewel led to a long article on a topic that has been of great interest to me, and has now appeared in the Journal of Number Theory [in fact, writing this paper has been a valuable academic experience, and some day, I am going to write a blog post exclusively about it]. Jishu has multiple papers under review, but here's something that makes me happy and proud: Student 2, Neha initiated a nice research project with him and their article has now appeared in the Journal of the Ramanujan Mathematical Society.
I would like share a few reflections about PhD supervision.
1) Student first.
Student supervision is not exactly smooth. Since I live in Pune, I can't help but compare supervision to driving on rough roads full of new speed breakers (which weren't there yesterday), not to mention the change in the entire landscape due to the ongoing metro construction. Roadblocks can either occur due to difficulties in the projects, and or due to a complete contrast in the personalities and priorities of the mentor and the mentee. Since mentees in this case are adults with minds of their own, there will likely be many situations of disagreement, or when the student just refuses to act as per the expectations of the advisor (or vice versa). When ego issues find their way into this mix (a perfectly human thing to happen), it is easy to forget the overriding goal, namely the training of the student.
The role of the guide is to train the student, make the student aware of opportunities and "advise" the student about issues to which they have limited exposure. The key goal is to initiate the student into the scientific journey. But, at the end of the day, it is an advisory relationship where the student may have a different path in mind or a different style of traveling from what the guide may have envisioned. For example, the student may not be so keen on the research project that the guide has suggested, but may have built collaborative networks for a different project. Is the guide to be like a nagging/overbearing parent who insists that the student do everything exactly as they want? Or, is the chief guiding principle to be what is best for the student so that they get a degree and move on in life?
The "nagging/overbearing" persona does have its advantages occasionally: it has to be turned on when the student is procrastinating before submitting something, not compiling their thesis in an acceptable format, or when their idea of preparing conference talks is to copy their papers onto slides (this is a perfectly natural thing to do for someone speaking on their work for the first time). How much and on what matters the guide is to persist depends on the situation at hand (will the student lose their fellowship or visa status if a document is not submitted on time?) and the level of awareness in the student (is the student mindful of the consequences of not submitting something on time, or not doing something carefully?)
But, as a guide, the most important skill to practise is to tailor our reactions based on what is best for the student, namely that they get their degree along with the skills and expertise to move on. This is similar to dealing with the bumps, debris and traffic on Pune roads by remembering how our roads and public transport will eventually transform when the metro is fully operational. To carry the analogy further, do we want the PhD journey of a student to be like the metro (making progress and transforming Pune, day by day), like the failed BRTS project (took off, and then stalled), or even worse, the "proposed" Pune airport project at Purandar (which never seems to take off, even as multiple cities in India of all tiers get their own airports)?
2) Growing together.
The relationship between a mentor and mentee is that of synergy. We work towards a common goal, build ideas together and bring complementary skills into a project. The outcome is as significant for the student as it is for the advisor, even though the consequences for the student may be more evident. Every project that I have finished with a student initiates the student into a new research theme and questions that they may choose to focus on in their initial days before eventually developing their own vision. But, it also adds a new dimension to my own research programme. Many colleagues and friends assign a PhD problem to their student independent of their own research goals, and let the student take it forward on their own with some guidance. Perhaps, I may do this in the future. But, at this time, I find myself heavily invested in the projects of each of my students; I assign problems to my students that I've been thinking about myself. These problems have been of great importance and relevance to my core research programme. At a deeply personal level, each successful project that leads to a PhD not only opens a path for the student, but also renews my faith in larger goals. As such, we both become a part of each other's journey of growth.
3) Sincerity and mental flexibility matter the most.
All my students have very different personalities. Each has their defining strength, and looking back, I can now see how the specific strength of each student is demonstrated in their work. Each student also has their own struggles, and I have faced unique challenges in each relationship. Some students may demonstrate more creativity in their work. Some are willing to jump right into a problem, while others may need a little prodding in this direction. Some are extremely thorough with each aspect of their writing, while some like to get their work out as quickly as possible, and have to be gently encouraged to put more care into proofreading. Sometimes, the same student is very thoughtful while writing a paper, but not so while preparing a talk, or vice versa. Some can work on multiple aspects of a project at the same time, while some do much better focusing on one part at a time.
So, the other day, I tried to "rank" what qualities or strengths are most desirable in a student, or what "weaknesses" are the "least desirable". I could only come up with one conclusion: as long as the student is sincere about their work, has the flexibility to accept feedback and believes the guide to be squarely on their side, every attribute falls into place.
Sincerity in both the guide and the student is a vital part of the PhD journey. The student's sincerity manifests in their willingness to work, and the guide's sincerity manifests in them contributing wholeheartedly to the student's growth. This makes the interaction meaningful, pleasant and forward-looking, even with all the personality foibles. A trust develops that has the potential of surviving (and even flowering) through the years ahead.
In essence, what made each advisory relationship successful was the love for mathematics in each student and the fundamental willingness of each student to work hard and improve themselves through feedback. My eldest two students are now my friends: I feel happy when they make an effort to keep me updated about their professional journeys or when they reach out for advice. I have received valuable advice from them as well. Now that the youngest two have graduated, I hope that they will also see me as their lifelong cheerleader and well-wisher. Further, with every new student I supervise, I hope to become a better mathematician and a better human being.
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