Thoughts on a semester gone by

Some time in the middle of January, after concluding a three-month long stretch of nearly back-to-back travel (mostly for conferences), I was relieved to be back at my work desk. The Spring 2024 semester had just started, and a plan for the next four months (which, fortunately, did not involve any travel) had been chalked out: there was a course to be taught, and a couple of research projects to be pursued. Preparation had to be made for upcoming departmental evaluations, and plenty of reviewing work loomed ahead. In addition, buoyed up by my self-discipline (most of the time) in eating habits during this particular phase of travel, I resolved to give my best to personal fitness goals for the few travel-free months ahead. I now saw the "home front" as a valuable resource to be leveraged (and guarded zealously) for personal and professional goals. 

I've had varying degrees of successes and challenges in different activities. Let me start with a mini-success: I've kept a regular running, Yoga and strength-training routine going over the last few months, in addition to a well-balanced diet. As a result, I am now down to a weight that I last enjoyed more than 12 years ago, and continue to make progress. Both my gym trainer and Yoga instructor have expressed satisfaction at my improvement in exercise performance and Asana practice; in fact, the Yoga instructor has encouraged me to move up to the next level of training. In June 2024, I will start training at the intermediate level (up from the newcomer to continuing beginner level at which I have trained until now) at Pune's most formidable Yoga institute, and have to make an even bigger commitment to regularity, concentrated efforts and personal practice.

Yoga is not for narcissists. It gives you a sharp reality-check about what you've been doing to yourself all these years. It forces you to face your weaknesses squarely, and work on them with patience and humility. Needless to say, the larger goal of Yoga practice is for this attitude to expand to other areas of life beyond the Yoga mat, and life does give you plenty of opportunities (and hard knocks) to apply these learnings.

Post mid-semester, one challenge after another presented itself. Some of these challenges were pleasant in as much as I looked forward to doing the work to meet them. For example, one of my research projects is currently going through a phase of trial and error in which we are trying many different techniques to execute an important calculation. No sense of intuition is coming to our aid to suggest a way forward, and we continue to hammer on. Another interesting thing that happened was that in my class of six well-prepared and motivated students, we managed to finish more than 90 % of the syllabus before the midsem. Based on student feedback and requests, we moved to an advanced topic which was, frankly, quite new to me as well. The lecture preparation took very long, and cut into the time reserved for other work, including research projects, but has been a valuable learning experience (certainly for me, and hopefully for the students as well). Nevertheless, challenges in research and teaching only motivate us to work harder, and every little step of progress brings joy.

The problem arises when academic challenges such as the above are overshadowed by other incidents that are not in alignment with our professional training and goals. In the last couple of weeks, the institute collectively faced an unexpected and distressing situation, which drained out a good deal of energy and enthusiasm from many of us. As I prepared myself to face the situation with patience and resilience, it took much of the sheen off my academic activities: my primary energies, which should have gone into research and teaching, were now occupied in apprehending what was to come next. Thanks to the persistent efforts of our registrar, and proactive engagement by some of my colleagues, the situation is now resolved. 

I wish I could say with honesty that I welcomed the new experience, and that I am grateful for it. But, I cannot. The only silver lining through this whole episode was that it taught me to show up for everything else in my schedule, including research, teaching, and workout sessions without making excuses. It also taught me that however terrible or anxious you are feeling, spending time doing math and pursuing fitness activities (basically, following your structure to meet your own goals) helps. Sometimes, "self-care" just means getting your work done so that a situation does not get worse. This was my lesson for the semester: how not to make things worse for myself and others.

On dreaming versus preparing for nightmares

The other day, a friend, while preparing for a trip to a city in USA, mentioned that he was nervous about the travel. This was surprising to me: this is a well-traveled, resourceful person, with travel experience to numerous countries (including a good number, where he did not speak the native language). What's more, he has managed multiple travel crises through the pandemic. For example, in a previous trip to USA, his flight from conference-city to New York got canceled (one among 1500 flights that got canceled in USA on that day).  He could not find a bus reservation and the train journey was not an option as a building had collapsed on the railway track. Through all of this, he managed to reach the New York airport a few hours in advance, and worked his charm on the check-in staff to get transferred to another flight (at no additional cost), which brought him straight to Delhi instead of a long haul at London Heathrow (which, as we all know, would have been another disaster). With this experience, I reminded him how he was the "Travel Ratna" of our social circle, but the encouragement did not work much. 

Was he growing old, he wondered. Or, was the concern coming from the vast outrage factory called social media? Or, was he just tired and needed a good sleep before starting the 26 hour journey (including airport transfers)? Last I heard, he has reached his destination safely. He  informed us in our WhatsApp group that it was one of the most pleasant journeys he had made. He walked comfortably to a hotel nearby, and realized that all the social media fears about the city were grossly exaggerated. We hope he has an equally pleasant travel back to India. Nevertheless, I completely relate to what he was feeling.

This made me think: as students, we used to take travel mishaps in our stride, or at the very least, not worry about them so much beforehand, even while living on a shoestring budget. As a grown up, on the other hand, with far better finances to handle adversities, I often find myself ruminating elaborately on things that can go wrong. Like the gentleman above, I also wonder if this is a function of getting older and `less' indestructible. Or is it that in the post-Covid world, with airline botch-ups far more frequent than we have been used to, and the airline staff far less efficient and polite in dealing with them, it's impossible not to think of what can go wrong?

Why have some of us turned us into the kind of people who no longer dream of the exciting possibilities of journeys to interesting destinations for interesting reasons [even though we say yes to invitations and plan for such travel as a matter of course]? Why do we keep thinking about what could go wrong until we are back home? Did the sudden, unexpected onset of Covid, in which the world had to live with uncharacteristic arrangements and unexpected losses for more than 2 years, make our collective resilience brittle?

Facing challenging situations makes us strong and resilient. But, it can also make us wary of having to face similar situations all over again, now that we are aware of the immense possibilities of things going wrong. How many of us say, "hello adventure, come get me" before starting a long travel, versus those who start by saying wistfully, "hope this won't be as bad as the last time"? And, in all honesty, how many are still able to take the middle ground and say, "let's take a step at a time and see what happens" without feeling queasy?

I tend to gravitate between the second and the third category. Before any long journey or multi-city travel, I break things down into "small steps" and list them out. A step could be as small as getting through the security counter. Then, as the journey proceeds and each step gets completed, it is "checked off the list". With each item checked off the list, I feel better. I also try not to think later about what went wrong during a step as long as the step gets completed eventually. This is hard, but I am getting better. Basically, I am trying to organize things with a hope that breaking them down into small steps also breaks down unexpected shocks into smaller, tolerable shocks. That is, I try to take one step at a time and hope that even if something is "as bad as the last time", the shock will come in small instalments. Perhaps, there is a hidden hope that anticipating potential shocks can lead to happiness when the shocks don't come. 

But, why be so obsessed with shocks? I hope to work my way back into the first category of "hello adventure, come get me"people. I want to be that person again who dreams of the exciting possibilities before starting, and not the person who laboriously prepares for nightmares. But, was I ever that person? I hope it is not too late to be so for the first time. 

Finally, may I just say that whatever was written above about travel is a metaphor for a lot of situations I am facing right now, including challenging research projects?

Tales of a teacher

A few days ago, I realized that I have now been teaching for 20 years. I taught my first course in the Spring of 2004, as a 23 year old PhD student. Once the teaching committee at my university identified grad students who could do a reasonable job on the blackboard and were ready to face large classes, they would give us an option to either teach a full semester course, followed by a teaching-free semester, or perform teaching assistantship duties such as marking and tutoring for both semesters. I chose the former option. My very first course as an instructor was in the year when I was to take my comprehensive examination, which would determine if I could stay on for a PhD or not. 

This was a service course in linear algebra for a class of around 80 students: most students taking the course were from other departments, and had to take this as a required course. Many students were in the senior years of their programme. So, it turned out that many were older than me. Some had decided to start or resume university studies after several years: in some cases, their children were in university at the same time, and would help them with the assignments. I continued to see this phenomenon through all the years that I was in Canada. Teaching in Canada gave me a chance to experience their culture in a unique setting. I also learnt how much these people valued politeness, kindness and sensitivity. On one occasion, for example, an older student was concerned that I was looking unwell, and offered to drive me to the medical clinic, as there was heavy snowfall outside. Students would regularly show up for office hours, and apart from working on their assignments, we would occasionally discuss other parts of our lives: this is how the class came to know that I was getting ready to face the dreaded comprehensive examination. On the day of the exam, a large part of the class showed up for the "public" part of the exam: the research proposal had to be presented in a 20 minute presentation. They probably did not understand any part of the talk, but showed up to support and encourage me. I deeply value this memory. 

I taught again the next year; this time, I was teaching a course in Complex Analysis to 100+ engineering students. In complete contrast to the previous class, these were a bunch of brats: this was the only class I've ever taught where I had to request students to not whistle in class [1]. After a few lectures, a sombre mood prevailed in the class. Complex Analysis has this effect on most of humanity. We started getting on well, and the course proceeded smoothly. One other crazy experience with this batch was on St. Patrick's day (or was it the morning after?) While half of the class was absent, the other half showed up drunk. Let's just say that thanks to this class, I had the "now, I've seen it all" moment quite early in my teaching life! No other batch of students has come close to putting me through what this class did.

The year after that, I was getting ready to defend my thesis. I was again assigned the same course in Linear Algebra that I had taught before: this time, the students got to know about my defence date [2], and some showed up for the public presentation. To make the presentation more relatable to them, I kept using words from linear algebra such as finite dimensional vector space, diagonalizable linear operators, basis of eigenforms etc (in the context of my thesis work, of course) which made some members of my defence committee smile. Incidentally, my class was scheduled soon after the defence, but I had requested a friend to cover for me. While the students sauntered down the hall after the presentation, she waited outside the defence room while I went through the closed-door exam. We cut a celebratory cake with some other friends after I was declared a "Doctor", and she ran down to teach my class, while I sat numb and dazed in the lounge [3].

My teaching reviews that semester were filled with congratulatory messages. In these reviews, I got some of the earliest reference letters of my career: several students recommended that I be hired as a "full-time" professor. 

My first faculty position (or as my former students would put it, my first position as a "full-time professor") was at IISER Kolkata, which was then functioning out of a temporary campus on the ruins of an older university. For my very first course, we did not have a classroom. So, some chairs were arranged next to a board in a computer lab. While the students were excellent and super-motivated (one of the best things I like about being at an IISER), one vague memory I have is of the director or some HOD often walking into the lab with a prospective faculty candidate to show them the computational facilities. The candidate would often shoot a confused glance when they saw me lecturing to a handful of students, while people worked on their computers in the other half of the room.

For the next batch, I managed to get a classroom. It had a pillar right in front of the board. Every single day, I had to resist the temptation to swing around it like Shah Rukh Khan in Swades (in case you don't know which scene I am talking about, watch here from 2.25 onwards). Sometimes, clueless goats and cows would wander into our classroom. I was fortunately spared the experience of snakes entering the classroom (they seemed to have a preference for labs, hostels and faculty homes, including mine). On one occasion, due to a failure of coordination between IISER security and that of the university that we were functioning from, the building gate was locked with all of us inside. Again, I have a vague memory of it raining and the mobile networks not working: so, it took a while for someone to come and let us out [4]. The good thing is that with all these shared experiences, this batch and I developed a special affinity: students from this batch still call me up or email me on Teachers' Day, and also stay in touch with me. 

Soon, I moved to IISER Pune. Almost all my teaching has happened here. In the 20 years since my first course in the Spring of 2004, I've now taught all kinds of courses at many levels: from first year undergrad to PhD students, with class sizes ranging from 2 to 200, including general, introductory courses, standard courses for math majors, specialized topics courses (one of which led to writing a book) and PhD-level courses. Fortunately, I never again had to deal with students whistling in class, or showing up drunk (not that I know of, anyway). I occasionally see people scrolling on their phones or falling asleep: but that is okay, as long as they do not disrupt the class. 

The pandemic teaching was an entirely different experience: for nearly two years, I lectured to an empty class, my lectures were recorded by the staff members from our Science Media Centre (who, surprisingly, never fell asleep in the lectures) and the recordings were shared with students. 

One of my most recent experiences was in Autumn 2023, when I taught probability to a large class of 200 students. I was curious about this experiment: I was teaching probability for the first time, and to a batch of students who had finished the last few years of their school in online mode due to the pandemic. In addition, many of our students in the early years have not had mathematics in Classes 11th and 12th. The course had its challenges, but was successful overall. In fact, the teaching reviews indicate that I seem to have taught long enough to develop a sense of humour.

In complete contrast, this semester, I am teaching a course on Fourier Analysis to a small class of 7 math majors in the fourth year. Thanks to their previous preparation and high motivation levels, we finished more than 90 percent of the syllabus before the midsem. So, we now have the freedom to explore more advanced topics. I am using this opportunity to learn a new topic and teach it to them as well, namely Fourier analysis and the theory of uniform distribution on compact topological groups. Fourier analysis mostly focuses on one particular such group, namely the unit circle. From what I am learning so far, showing it all as a special example of a more general theory makes the treatment of the subject neater and more elegant. 

This course (and the larger experience of teaching over the last 20 years) has taught me how closely intertwined the experiences of self-study, learning and teaching are. May this go on.

[1] "Request" is a euphemism. My exact question was: "Am I in a university class, or a fish market?" The whistling stopped, but some students told me later that they were confused by the allusion to a fish market. This seemed to be a uniquely cultural phrase, that is more relatable to Indians than Canadians. 

[2]  From their super-chatty prof, naturally :-)

[3] In retrospect, I suppose I could have pushed myself a little more to teach the class as well.

[4] If you visit the sophisticated, permanent campus of IISER Kolkata today, you will have no inkling of how it was in the early days.

Twitter threads (on life choices, long walks, movies and math)

I do not have many new things to write about from my part of the academic garden. Instead, I would like to put together some of my older X/Twitter threads on assorted topics such as life choices, long walks, travels, a movie, and mathematics. Here they are.

1) On authentic life choices: Some time ago, a younger colleague in her early 30s was a little upset. "I've been made to feel that I'm too energetic, too excitable, too caring, too much in one way or another...like I'm a handful - not worth the trouble", she said. This reminded me of receiving similar comments when I was at her life and career stage. This made me reflect on how life evolves through the 20s and 30s, and how the authenticity in our choices has a bearing on 40s. This led to the following thread: link.

[Note: I use the 20s, 30s and 40s only as notional place-holders in a strictly limited and personal context. The timelines are different for each individual.]

2) Trek to Matanga hill and parallels with a life in science: Hampi is a beautiful travel destination. It used to be the centre of the Vijayanagara empire several centuries ago. Exploring the temples, monuments and the overall landscape of this region is an invigorating exercise that brings us closer to our history and heritage. In 2022, I wrote a thread on a long walk/trek up the Matanga Hill. The trek made me reflect on many parallels with a life in research (more generally, a life in any creative pursuit). I wrote a thread on these reflections: link. 

3) Another nice walk in Hampi: Hampi has several paths for those who like to go on long, meditative walks. Our favourite walk is on a trail from the Virupaksha temple to the Vitthala temple complex. We took this walk again in December 2023, and I wrote a thread here: link.

To my pleasant surprise, this thread received a lot of engagement. Many people shared pictures and stories from their own trips to Hampi, and also suggested other long walking/hiking routes which we hope to explore in future trips. 

4) A trip to Srinagar: Based on a recent trip to Srinagar, this thread is very close to my heart: link. I enjoyed every aspect of this trip: the beauty of Kashmir, pleasant interactions with eager students and the Kashmiri community, and the revival of memories from previous trips 25 years ago. For some strange reason, the link to the above thread misses two tweets at the end: see here.

I hope and pray that the people of Kashmir can overcome the long decades of struggles and challenges that they have lived through, and can move forward to fulfil all their dreams. 

On a related note, the trip also made me think carefully about my career goals and mathematical activities that matter. These reflections were also shared in this blog post. 

5) Biopic on Shakuntala Devi: On a lighter note, in 2020, I wrote some comments on the movie "Shakuntala Devi" (starring Vidya Balan in the pivotal role): link.

This led to another thread. 

6) On some exceptional Indian women mathematicians: Shakuntala Devi is often described in popular culture as "India's most famous woman mathematician". But, what does it mean to do mathematics? Is mathematics all about performing massive computations? Or is there more to it? I wrote a thread here, elaborating upon these questions. The thread contains stellar examples of some inspiring Indian women mathematicians who have made a big difference through their research, teaching and mentoring. The thread was written for India Wants to Know.

7) The early days of the Journal of the Indian Mathematical Society: While gathering information for a biographical piece on the distinguished number theorist Sarvadaman Chowla, I learnt about a rather surprising "enabler" of mathematical talent in the early 20th century. This source nurtured (and in turn, was nurtured by) many, including Ramanujan: The Journal of the Indian Mathematical Society. Here's a thread: link.

On a related note, my biographical piece on Sarvadaman Chowla appeared in the Bhavana magazine, and can be found here.

Do also check out the archives of the Bhavana magazine for high quality mathematics writing (essays, biographies, interviews and more). The writing is accessible to non-specialists who have an interest in mathematics, especially in the creative and cultural aspect. 

The week in "review"

In the last few posts, I have been sharing thoughts around academic reviews: is research productivity the only criterion that matters to a reviewer? Does time spent in mentoring or teaching beyond our institutional duties matter? Is it judged negatively? What does a review process (and preparing for it in any form) do for us (point (3) in this post)?

One of the reasons why this has been predominantly in my thoughts is because our department was preparing for an external review that happened in the past week. A group of six senior mathematicians visited us for a few days, and met us all individually as well as in a group in order to review how we were doing as a department. For the individual meetings, we were all encouraged to prepare a report on our academic activities in the last five years, and a presentation on our recent and future research goals. The emphasis of the presentation was to be solely on our research work. This was a serious exercise, and we spent hours figuring out how to explain our research work to the committee (which would not necessarily have specialists in our field) in a comprehensible manner in under 10 minutes. With the adrenaline rush of students preparing for their exams, we worked to prepare the slides. Over short coffee breaks, we discussed this with friends and made philosophical remarks about what this was doing to us [1]. 

My individual meeting with the committee was pleasant beyond my expectations. After hearing out the presentation and a brief discussion on research work, the committee asked me a question which I was not quite prepared for: "Are you happy?" When was the last time someone asked me this question in my adult life, I wondered [2]. I had an affirmative answer to this question (and truthfully so), and we went on to have a friendly conversation about related issues such as teaching and student supervision. 

One other amazing thing about this meeting was that two of the members had informally mentored me before I moved to North America for graduate studies. Neither of them had taught me directly, and while one of them was a faculty member in a department where I studied for a few months, I met the other one in a summer school organized by them. Looking back to that time, I don't believe I showed any unusual talent or ability. I just had a strong interest in pursuing mathematics, and needed to know how to continue doing it: both these members gave me the gift of their time, attention and advice when these were needed the most. It is likely that members of the committee had had a similar interaction with some of my other colleagues. An important take-away from this meeting, therefore, was that my fear about being judged negatively for spending time on mentoring or outreach activities beyond research and teaching at IISER was unfounded because it was clearly something that these members also care for [3]. 

Later in the week, the committee met us all as a department and we had a lively exchange of ideas about our larger goals and challenges. The committee members also talked frankly about facing similar challenges at earlier stages of their careers, and once again, one could not help but appreciate their gift of time and attention to all of us.

While this review process undoubtedly turned out to be a great experience, not all reviews have such positive outcomes. Occasionally, feedback or suggestions received in a review process of any kind, be it from an article referee, grant agency, audience at a seminar or even PhD advisor/mentor may not align with how we think and work. Sometimes, we may not receive timely, or well considered feedback at all. Recently, I listened to an episode of the podcast Pratidhvani, in which the guest, Professor Suresh Govindarajan described a challenging situation during his PhD days, when his advisor chose not to give him timely feedback on his work. In addition, the advisor made a suggestion that did not align with the student's value system.

PhD studentship is one of the most vulnerable phases of life; the final phases of PhD, when your research needs full, one-pointed attention, is also the phase when you have to worry in real time about where you will go next. The role of the advisor, particularly in terms of providing meaningful and regular feedback on your work, in order for you to finish the degree and move on to the next stage of your training, is extremely important here. What if the advisor chooses not to provide such feedback, or to provide it in a manner that is not helpful at all? How Prof. Govindarajan coped with the situation is best heard in his own words (56.43 onwards on the podcast is when this particular situation is described).

This is what I am going to take away from the above episode and from all the reviews I have been through: feedback received in a review is temporary, based on what a particular reviewer (with their own expertise and perspective) is evaluating in a given situation at a given point of time. We should receive it in that spirit. It is not a " permanent indictment" on our whole state of being. Our own performance keeps changing and evolving based on the resources available to us, and the environment we are in. For example, someone who is seen to be struggling while at one department can blossom into their full potential in another department with a more supportive work-place, or where they have people to talk to and collaborate with, or where they simply feel happy. It is difficult to see a review as something temporary, especially if it is negative: human nature is wired to hold on to criticism, and overcoming this tendency feels like a task of Yogic proportions. 

In the context of academia (as perhaps also in the context of a vocation based on the creative arts), a safe coping mechanism to handle reviews of all kinds (good, bad, non existent) is the way of authenticity. What our work means to us and how we want to do it can only be determined by us; it has to be anchored in our own sense of self, our own honest self-evaluation of our work, and our own innate desire to grow. With this in place, an external review, if provided constructively, can bring more clarity in how we can do our work better. It can be a means of encouragement and even inspiration. If the review provided is not constructive, but well-meaning, it may not be as effective, but certainly deserves a sense of gratitude for the reviewer who spent time and energy trying to provide one. 

Handling malicious or unethical reviews is a test of resilience. Here, I am referring to situations where the review cannot be ignored, comes from a party that wields a position of power over you and is not immune to misusing that power to your detriment. I still don't know how I would handle such a situation. Maybe, I won't know until I find myself in one. May we all have the strength, the gumption [4], the resources and the support to handle such a challenge without giving up on ourselves, our values and on what we love. 

[1] For starters, it brought out (or reminded us of) the exuberant, childlike enthusiasm that brought us to mathematics in the first place.

[2] In my own case, by adult life, I mean life after starting an independent faculty position. 

[3] One of these days, I should do a focused, self-therapy session to figure out where this "fear" has come from.

[4] Gumption, not defensiveness.

On work-travel balance and other matters

In the early days of this blog, I would sometimes write "random" posts, that is, posts with short snapshots of multiple work-life thoughts (see, for example, here and here). I am reviving the random "series" again. Here are some thoughts on work-travel balance, accountability to goals, and facing the reviewer "within". 

1) After several days of travel across India (from Kashmir to Kerala), mostly for work, and occasionally for a break, a relatively calmer and more stable routine at home has brought some relief. It's great to be invited to deliver talks, and to travel to interesting destinations, but if we don't balance it with quiet, focused days at the study desk, how will we have new things to talk about? A well-structured life at home is great: you have a regular work routine around your research work, teaching schedule and meetings. You wake up in the morning thinking about the sunrise and next steps in your projects (or the lecture material for your next class), and not about the next flight to catch.  This makes it so much easier to focus on "deep" work. You get to have your cups of coffee exactly the way you like them and at the times you want them. You have complete control over your meals and over your work-out schedule (and access to the gym).Nevertheless, at this career stage, travel is only going to get more frequent in the coming years. One will have to flexibly adapt to different routines and time zones, not to mention, meal options and coffee times (if, at all, coffee is a possibility). One will have to learn to stay calm while dealing with the vagaries of flight delays, missed connections, cancellations, airport transfers etc. 

I believe that in this phase of travel, I made a lot of progress in dealing with all the disruptions and changes. I prepared all my talks well before the travel, and this itself took a lot of the stress away [1]. While I relish my early-morning coffee at home, I no longer feel disturbed when I can't get it. I do manage to make healthy meal choices based on what is available, and have also learnt to travel with a Yoga mat and Yoga props (which can be easily folded into the suitcase). Pretty much anywhere in the country, academics are blessed with good campuses with safe and pleasant routes to walk/run on. So, I have learnt to be responsible about my health while traveling. If I could develop the resilience to show up to my morning writing hours with focus during travel, the work-travel balance will essentially be sorted out. Question: is it possible to adapt to travel so seamlessly that one doesn't feel any difference between being at home and being away from home? 

2) Talking about Yoga, last week, as I was recovering from a hard day at work, I had this sudden wish to miss my Yoga class. I wrote to the instructor with a request to record the class, which I would practice later on my own. However, within a few minutes of the start time of the class, I started feeling very restless: it felt as if I was missing out on something substantial: so, I did show up for the class and participated in the remaining part of the class. I was sufficiently rejuvenated after the class to prepare two classes for the math course that I am teaching this semester. 

The next day, I went about my routine as planned, and wondered what would have happened if I had indeed missed the Yoga class. In addition to the mental regret, it is almost certain that I would not have practised it on my own, thereby missing important instructions that would be needed in the next class. Or even if I did, I would have had to carve out an hour away from some other activity, and then, there would be a cascading effect of making up for lost time in a variety of urgent activities. Some important activities would have to be put aside for later. Unlike a rolling stone that gathers no moss, rolling time schedules do gather moss, and the time taken to finish an activity only increases with each postponement. Showing up with a sense of responsibility and accountability, and not caving into the "all or nothing" approach keeps the days rolling smoothly. 

3) A strong motivating factor in showing up for scheduled activities every day is to remember the larger goals. But, for that, one needs to have larger goals. In different conversations with two colleagues recently, we discussed this point.  Some activities that force us to reflect on our goals are writing grant proposals, and preparing evaluation reports. Both of these activities help us to think about our vision: what is our story, and in what direction are we taking it forward? How is the story shaping up, and what parts of the story need more development? In many cases, when we write for an audience who are not necessarily working in our area of expertise, we also have to compose and present our goals more creatively. Well before we hear back from the evaluation committee or the grant agency, our own "inner" reviewer gives us a fairly accurate feedback on where we stand as researchers, provided we care to listen. Among my friends and colleagues, we share a lot of jokes (and internet memes) about writing grant proposals: but, I have never felt that time spent on writing one was wasted (even if the proposal was not successful). In fact, on a recent occasion, I finished a research project with my PhD student based on one of the goals I had written in a proposal. As a pleasant surprise, I heard about the acceptance of the article as well as the successful approval of the grant around the same time. This was so encouraging: I am now motivated to develop the other parts of the "story" of which this project was a part. While writing the grant proposal, the co-PI and I had a very good feeling about it: our "inner" reviewers appreciated the honesty, clarity and sense of purpose with which we wrote it, taking into account our respective expertise and the themes that could be developed in collaboration. Even if the application was not successful, we promised each other that we will continue working on these ideas. But, as it turns out, the peer reviewers also felt the same way about the project: we got the entire amount we asked for, and it will enable us to hire two postdoctoral fellows to join our project. 

This was a rare occasion when our evaluators agreed with our own inner assessment of our goals and work. Papers and grant proposals get rejected frequently, and often, the reviewers may not share our own assessment (and this can go in both directions). Most of us just get on with it, especially if our inner reviewer gave us an honest feedback (good or bad), and we have a healthy mechanism to face it. It makes me wonder: when we feel a strong sense of revulsion towards review or evaluation in any form, do we fear confronting the external reviewers or the reviewer within?

[1] Yes, I have had phases in past life when I prepared for talks during flights, but have given up on this in the interest of my mental health. If one really needs to work on a flight, the no-internet time is much better utilized by working on new problems.

Tales of a PhD advisor

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.