Not your Ma'am

 Reflections on a few things that I was thinking about in January:

1) Not your Ma'am

The other day, someone on X (formerly, Twitter) left a reply on a tweet. Soon after that, they left another tweet apologizing for not addressing me as "Ma'am". This made me think more about appropriate ways of addressing faculty members, senior colleagues, peers that we are communicating with for the first time, and of course, people with whom we interact on social media. I think I can reasonably assert on behalf of almost all my colleagues (and especially those of us who are on social media) that we do not expect to be addressed by honorifics such as "Sir" or "Ma'am". At IISER, several students address their teachers by their first names. But, many students prefer sticking to the time-honoured tradition of "Sir/Ma'am".  

Professional, polite and mutually respectful interactions involve more than modes of address. While it's not exactly rocket science, this aspect does involve more effort than choosing a form of addressing each other. It includes, for example,

A) writing emails with complete sentences, 

B) showing up on mutually decided meeting hours on time or letting the other person know in advance of any delay or change in plans, 

C) making reasonable requests (such as informing the instructor well in advance if you are requesting for a reference letter, providing them all the documents that will help them write the letter and following up closer to the deadline), and 

D) learning to conduct smooth discussions on matters of disagreement (such as when the student and the instructor differ on the grades that the former should receive, or when two colleagues have a difference of opinion).

The above contribute much more to an atmosphere of academic freedom and meaningful exchange of ideas than choosing (or not choosing) to call someone by name. 

Some (not all) of my senior colleagues insist on being called by their first names, and can even be a little fanatic about it. They feel that if a younger person is addressing them with titles and honorifics, it will prevent them from freely sharing their thoughts. The younger folks do not necessarily believe this to be the case. I have never held back from expressing my views based on how I am addressing the other person: obstacles to free expression usually arise from how the other person reacts, especially if they are in a position of power over you [1]. 

At the same time, I can see a distinct advantage in insisting early on that your younger peers call you by name. When former students and mentees become colleagues, it is unbearably awkward to continue to be called "Ma'am" by them . But, it is also awkward for the younger person to change the mode of reference.  Nevertheless, the change has to be made, and it's probably easier to do it sooner than later [2]. 

It is totally okay to call your instructor by name (especially if you are making an effort on Points A-D, where the real work lies). It's even more okay if you pronounce/spell the name correctly.

2) The choice will make itself

The spring semester is a time of great churn. Our second year BS MS students are now in the process of making a decision about what they want to major in. The PhD admission and postdoctoral application season has started. Many people, while navigating between different entrance exams (such as NET, GATE, NBHM etc) and multiple applications, are trying to determine whether they want to walk down the academic path or consider alternative careers. In many cases, there are at least two options that look equally attractive. In some cases, one option seems to be what they really want, whereas the other option appears to offer better worldly benefits. A common conundrum among students who talk to me is to choose between majoring in physics versus mathematics. "I like both the subjects, and the thought of choosing one over the other is causing me a great deal of anxiety and FOMO," said a student. 

As the person in most of these conversations who has been through the process a "few" more times than them, my advice is that they keep brainstorming the advantages and disadvantages of each choice. That they use this as an opportunity to sharpen their decision-making powers by considering multiple angles and perspectives. That they also use this as an opportunity to draw within themselves to recognize (possibly for the first time) what will personally make them happy. I am reminded of a silly dialogue from a movie that had come out when I was about to start my Master's. "Close your eyes," said a character to another. "Who do you see? That's the one for you." Go ahead, adapt this principle to your career choices as well, I joked with a student. Close your eyes, and imagine you are in a beautiful, cosy study room with a big window and a view of beautiful mountains with sunlight filtering in. There's a hot cup of coffee next to you. What do you see yourself doing? "I see myself working with a pen and paper," said the student. To me, that pretty much seals the choice. But it could also mean theoretical physics, the student suggests. 

One cannot deny the absolute importance of individual agency in making life decisions. An unrelenting, thorough reflection on our choices sharpens our logical reasoning, mental resilience, and self-awareness. It gives us the courage to take complete responsibility for our choices (to completely "own them", in popular parlance).  But what finally happens is also based on several factors beyond our control or current knowledge. Can you predict that a pandemic will break out? Can you possibly foresee a diplomatic storm ensuing between your country and the one you wanted to study in? Did the flight/train to your job interview get cancelled [3]? Did the professor you wanted to work move away soon after you joined the university?

On a more pleasant note, while you are more or less ready to move to Field A, you may suddenly end up listening to a beautiful lecture in Field B that will miraculously change your mind. You may meet a wise person during a journey or a conference (or both) who will make you re-evaluate your priorities [4]. 

One must think carefully about all of our choices. At the "moment of reckoning", however, it is highly likely that the choice will make itself. 

3) Give it time

Social media recently erupted with discussions about 70 hour and 90 hour work weeks. Such discussions often touch a raw nerve, as most of us navigate multiple demands on our time, and there is always unfair judgement on what we choose to allot less (or more) time to. 

If we sign up for something or accept a responsibility, there is no substitute to giving it the time that it needs. Every aspect of work, personal or professional, needs time. We hope that before taking something on, we carefully consider the time that it will take, and then take a call based on the availability of time to us. But, more often than not, a task takes longer than we thought it would, and as functioning adults, we do our best to rise to the situation. 

Solving new problems or proving new theorems is that aspect of a mathematician's work that takes much longer than one thought it would. We lose track of time spent on it, and I have never heard any scientist complaining about the amount of time it took them to finish a project: this is often narrated with pride and joy. On a similar note, I have never met a colleague or friend in academia who complained about devoting time to preparing good lectures, either for their courses or for conferences/seminars.

There are other parts of our job which also take time: peer review (including referee reports for journal submissions, writing reference letters for job candidates and PhD applicants), committee work, and mentoring students who may not be directly working with us but reach out for support or guidance. Our reputation is built on the integrity with which we execute these tasks, and all of it directly depends on how much time we allot to it. 

In the last few years, I have blogged a lot about learning to bring structure and consistency over long periods of time to meet goals that seemed challenging. Occasionally, I have also reflected upon how long it takes for growth to happen and for something to come to fruition: a research idea, a book, or career milestones. My personal growth and mental health have skyrocketed after I made a simple pact with myself: that I would give any task the time that it needs without judgement or anxiety. 

It seems that both the industry leaders who brought up the issue of work hours wanted to encourage their employees to have ambitious goals befitting their abilities, and devote the time needed to meet those goals. Instead, at least one of them ended up issuing statements that sounded condescending and even crass. Framing your views thoughtfully before communicating them also takes time.

Footnotes:

[1] Here, I do have to admit, albeit from personal experience, that there is indeed a strong overlap between those who prefer to be called by name and those who accept opposing points of view without going ballistic :-)

[2] The Bengalis seem to have evolved a working solution to this problem: they follow the middle path, and simply add "Da" or "Di" while calling older people by their names. This can remain constant even as one graduates through different career stages,

 [3] This has happened to me. On a January morning several springs ago, I boarded a flight to go for a job talk in another city, but the flight never took off. The runway was being used by some aircrafts for Republic Day practice. 

 [4] Yes, it does sound over-the-top, but both have happened to me, and to some others I know.

On conference talks and editorial duties

"Explain 2024 for you in one word,"  demands my social media timeline.  Conciseness is not my strongest quality.  So, I am going to sum up two years, 2023 and 2024 in two words: talks and reviews. 

(Conference) talks: In early 2023, I was invited to deliver a mini-course in a number theory workshop at NISER, Bhubaneswar.  I chose one of my favourite themes, central limit theorems in number theory, and prepared the lecture notes and slides with great enthusiasm.  Underneath the enthusiasm was a pressing need to present as much material about this topic in as short a time as possible.  "How do I present all the important theorems in this field along with all the proofs so that every minute counts for the participants?"  Further underneath, of course, was the "real" desire to present all MY results on this topic.  After the first lecture, I was taken aback when my host gently pointed out that I was going too fast. I slowed down in the second lecture, but received the same feedback. So, for the remaining lectures, I did the sensible thing of slashing down the content to less than half, and focusing on a few essential principles with applications. These lectures saw a far higher engagement from the audience. After giving up the self-imposed pressure to present everything I know about the topic, I felt relaxed. 

That evening, I walked back to the guest house with Professor Michel Waldschmidt, a distinguished number theorist who delivers excellent lectures, and is possibly one of the friendliest people on this planet. I confessed a form of impostor syndrome: an innate fear of being judged for not knowing enough if I don't present everything I want to. This was pushing me to present more than what a handful of hours could reasonably contain. I received valuable advice from him, which helped change my attitude.  

Through 2023 and 2024, I have put in some thought and practice into pitching my talks at the right level, keeping the content substantive but pleasant, and ensuring that I do not exceed my time slot in any lecture.  This requires better self-organization than I have practiced before. My most recent talk was at a number theory conference in Chennai two weeks ago. I wanted to talk about the project that I have spent the last few months working on. There was a real danger of devolving into technicalities. Without any fear of judgment, this time, I spent the first 25 minutes talking about the application of a classical technique to the most basic L-function, namely the zeta function, as the best features of the technique can be demonstrated here. I used the last 5 minutes to discuss how the idea can be adapted to the functions of my interest, namely the modular L-functions, and the technicalities that emerge in this application. (Here is the link to the talk, in case anyone is interested; it starts at 1:18:52). In a most pleasant turn of events, Professor Waldschmidt was in the audience and gave me warm and encouraging feedback for my talk this time. I reminded him of our conversation two years ago, and he was thrilled to know that his advice had been helpful.

A thought to ponder upon: many mathematicians prefer to deliver talks on the board. This requires planning and careful thought: you cannot write on a board in 30-40 minutes what you can show on slides. Can you convey your work effectively without all the equations neatly lined up on your slides for ready reference? The impact of a properly organized board talk is miraculous. In some of the best talks that I've attended, the speakers manage to make it look effortless, and it can affect the audience as deeply as a well-practiced musical composition. For the year 2025, I plan to experiment with this form, and get some practice in concision.

(Review/referee duties): The other academic duty in which I have found myself spending a considerable amount of time is writing referee reports for journal articles. I am not sure I have the most efficient system to fulfill this duty, but over the years, I have been getting better at it. This is a job we do (and others do for us) purely as an academic service. It takes a sizeable amount of time; and in Mathematics, you simply have to sit down and verify all the steps and details, which can take longer than planned. A large part of our duties as postgraduate advisors is similar: we proofread articles and theses written by our own students or mentees and check all details before they submit their work. 

Sometimes, people outside our immediate academic circles send us their work with a request for feedback; this often reminds me of early faculty days when I started writing to some senior mathematicians for feedback on preprints. Some had never had any prior interaction with me. Almost always, they wrote back and shared extremely helpful inputs. There were also occasions when anonymous referees gave thorough inputs for my submissions, much beyond the "call of duty", so to speak. These inputs and comments not only improved the quality of the article, but also helped shape new ideas for future research. 

How do people manage their own thriving research programmes and also take time out to write in detail to people seeking feedback, I wondered. While a desire to help is perhaps at the root of their response, they must have very good personal work habits (and sturdy systems) to be able to do this effectively. Does this develop with practice and experience? Do we develop good systems in response to a strong sense of purpose to serve the academic community, or does one develop a strong sense of purpose by performing such duties, beginning perhaps in small measure, and increasing our capacity with time?

A brilliant example that comes to mind outside of mathematics is that of the celebrated scholar, Mr. Bibek Debroy, who translated several unabridged Sanskrit texts into English, such as the critical edition of the Mahabharata, the Ramayana, and several Puranas ('unabridged' being the key word here, given the size of these texts). In addition to being a prolific writer and translator, he actively read and reviewed books by others in need of feedback. In early November, after his demise, several younger authors paid rich tributes to him; they wrote how he would carve time out of his extremely busy schedule (his duties included being the chairperson of the PM's Economic Advisory Council) to read their work, provide feedback before submission, and also write reviews post publication. Read here a touching tribute by one such author, Abhinav Agarwal, who describes the deep impact of Mr. Debroy's interactions, reviews and feedback on his writing career. 

The end of a year is a good time to reflect on things that touched us or taught us something valuable. I have been thinking of scholars such as Bibek Debroy, as well as many others in the mathematical domain, who generously devote their time and energy to encouraging and guiding younger people through reviews and feedback. I am reminded here of something that Professor Aravinda, mathematician and chief editor of the Bhavana Magazine wrote to me when I joined the Bhavana team as a corresponding editor. 

While introducing me to the new role, he wrote: "If only we are sensitive to true people's truer sentiments, we can deliver an honest academic service to the world, stamped by the most authentic of documents, and inspire the future -- most importantly, enriching our own lives in the process." I often turn to these words whenever I have a selfish urge to give up editorial/referee-related work because it is "not counted for promotion".

One day at a time, one step at a time

An experience that most functioning adults face is that of building up a routine with great effort, only to have it come crashing down in the face of an unexpected adversity.  Sometime in the summer of 2024, I found myself in such a situation. A health crisis in my family meant that I had to stay away from IISER for about six weeks.  My family dealt with the crisis wisely by putting together all the support systems and structures.  We all did what was necessary, and somehow managed to keep our work lives going (even if remotely). In my case, that meant regularly corresponding with my students and colleagues, and taking care of other urgent administrative work (such as preparing budgets for conference grants, following up with our grants office, submitting course outlines etc).  But, I soon realized that I was unable to focus on anything that required "deep work": I could not concentrate on my ongoing research projects, and my usual writing routine could not withstand the shock of the situation. One of my collaborative projects was gaining speed at this time, and while I joined all the meetings, it was actually the collaborators who were pulling all the weight during this phase while I started blankly at the screen. 

After the family situation was better, I returned to campus.  Nevertheless, there was a thick fog in the mind, possibly due to the stress of the situation and several weeks of irregular sleep. I was finding it hard to recover despite being back on home ground. Soon, there was another month-long phase of travel, and the writing routine seemed at its lowest ebb.

The redemption came in September in the form of an eight-day-long vacation in Kashmir that I had planned long before the family crisis had erupted. I was to stay for the whole duration in a quiet hill station called Yousmarg, known for its beautiful meadows. While planning the vacation (or more appropriately, the stay-cation), I had hoped to be in a completely relaxed state of mind after a summer of conferences and paper submissions, and to possibly start something afresh. But, it was not to be: the version of me that reached Yousmarg was terribly anxious at falling behind in all her research projects, and was struggling with low attention span. This could not continue.

So, I made a plan: I decided to focus on just one project and devote a few hours every morning to it. I also planned to work on the project for the rest of the day, but the latter part could be more flexible, combined by walking around Yousmarg, reading [1], or taking a nap, based on my mood and energy levels. The strategy was to start small and do a little bit every day.  In fact, I started with proof-reading some parts that had already been written by my collaborators, and promised not to judge myself even if it took me all day to understand some steps of a proof.  The important thing was to make some progress everyday, and regain my attention span in small increments.

It worked! 

The lack of internet at the hotel worked like elixir for someone looking to regain their attention span. I waded through all the project-related material (downloaded before the travel), line by line, step by step. Since I could not type on Overleaf or connect to my collaborators, I made notes and zeroed down on a couple of points that looked troublesome. The walks around the hotel became more pleasant while I thought these points over [2]. 

By the end of my trip, I found myself up-to-speed with all that had happened in the project during the summer, except for a couple of points. This may well have been the first ``vacation" in which I got to relax, while also working without anxiety. Soon after returning to Pune, I resumed my teaching duties (the post-midsem part of a second year course on probability to a large class) and regular meetings with students. At this time, I spoke to a friend who had recently overcome a similar challenge. She had survived a much more difficult situation, and was able to walk me through the different stages of regaining focus. "When the fog lifts, you will know; until then, one has to keep doing whatever we can."

While the ``fog" had still not lifted completely, the sunlight had started to filter in. My energy levels and attention span were both coming back, and the stability of not having to travel for the next three months motivated me to double down on the project. On the morning of the Mahalaya, I made a to-do list of literature search and writing needed to take care of some sections of the paper. The aim, everyday, was to not leave the study table until the task for that day had been completed. By the morning of Vijaya Dashmi, I had completed multiple sections, and had also corrected the points which were troubling me in Yousmarg. 

For those who know what I am talking about, these points had to do with some subtleties in the relationship between the symmetric-power L-functions for Hecke newforms and the Rankin-Selberg L-functions; with the corrections in place, all the subsequent sections had to be modified.  Our project is to find explicit constants in the zero-free regions for modular L-functions, and every estimate has to be noted and incorporated carefully and precisely into the "master" equations.  Soon after Diwali, our team of collaborators resumed our weekly meetings (we are working between three countries and four time zones).  In complete contrast to the summer, I was now eagerly engaged in the meetings, and would enthusiastically look forward to them through the day.  This is when I knew that the fog had lifted completely. We started working on each section, and over the last month, have cleaned up the manuscript and written out the proof of our main theorem. We are now in the final stages of the article, and the month of December will be spent in proof-reading and finalizing the draft. The feeling of showing up well-prepared for every meeting and absorbing all the insights from collaborators to improve one's understanding of the project is priceless. I enjoy working on this project every morning, and it is such a relief to have overcome the writing inertia of the summer months.

The writing routine is back, but with a realization that adversities and shocks can strike unexpectedly. Regaining one's focus requires kindness to oneself and some flexibility in work habits. It requires us to control where we spend our time and energy, but without slipping into victim mode (as my friend wisely pointed out). Above all, it is about taking one step at a time, one day at a time, consistently. If something looks intimidating (as it naturally will, if we are recovering from a situation which took us away from something we were doing regularly), break down the task into small steps, and focus on one step at a time without negative self-talk. Replace "Why I am I so stupid?" with "What exactly is the problem in this step?" Replace "Why am I so slow?" by "What progress have I made since yesterday? What can I do next?" If the next step seems to invite procrastination, break it down into even smaller steps. 

In time, we build things back (we really do, however "low" we start), and at the same time, become non-judgmental observers of our own growth and progress. For those of us who have to write regularly, the progress becomes visible in the form of all the new sections that were typed up. It can be quite revealing to compare the current version of something with what it was a month ago. While you were taking one little step every day (and possibly wondering if this was enough), your draft was growing bigger and more wholesome, the extent of which can be noted a month later.

Starting tomorrow, I will be busy with preparations for a major conference from 09-13 December at IISER Pune.  The rest of the month will be spent in conference travel and time with my family. Will I be able to guard my morning writing routine through all of this? And if there is a crack, can I bounce back to normalcy by taking one step at a time? We will leave these questions for a future blog post.

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[1] I specifically chose the letters and poems of Emily Dickinson because the Sangarmal hotel at Yousmarg, where I stayed, reminded me of her homestead. But, I may have chosen the wrong collection of letters. This particular collection contained many letters in which she is exhorting her friends, in moving language, to reply to her letters and not ignore her. These letters made me very angry with her friends, and may have drained my mental energies a little. 

[2] The walking, however, had other consequences. People in Yousmarg are extremely friendly; the thought of a (female) tourist walking all alone on a cold day is unbearable to them and they will take you to their homes and serve tea. The personal connections made through such interaction are invaluable, and sometimes, one just has to postpone the Math to the privacy of the hotel room and garden :-) 

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.

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 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.