On choices: reflections from two beautiful books

From time to time, social media erupts with debates about "right" choices and "wrong" choices. The subjects of the choices revolve around marriage, children, and lately, the working hours of a PhD student. I have often found these discussions leading to an angry (almost vitriolic) exchange of opinions. Somehow, this theme touches people in a rather raw way at the most vulnerable spots in their minds and hearts. This makes it nearly impossible to have a reasonable discourse on these forums.

In complete contrast, two books that I read recently presented thoughtful perspectives on the theme of choice, and helped me to reflect (without unnecessary noise and anxieties) on how we make and own our choices.

The two books, "The Memory Keeper's Daughter" by Kim Edwards and "The Real Deal: Lessons, Learnings and Laughter for Girl Scientists" by Karishma Kaushik belong to wildly different genres. The first book, based in Kentucky and Pennsylvania, is a fictional narrative spanning three decades from the 1960s to the 1980s. The second is the memoir of a contemporary Indian scientist who has experienced the scientific ecosystem in India and USA, and who has contributed to science in multiple ways: as a medical doctor, researcher, educator, science communicator, and as a leader of a national science programme.

"The Memory Keeper's Daughter" is based on a premise reminiscent of Bollywood movies from that era: Dr. Henry, who helps his wife deliver twins at his clinic, realizes that the second-born child shows signs of Down syndrome. While his wife is unconscious, he hands over the baby to the nurse, Caroline Gill, with instructions to take the child to a nearby institution. The wife, on regaining consciousness, is told that her baby is dead and has been cremated. Caroline, on entering the premises of this institution, is so revulsed by the atmosphere that she makes an instant decision to adopt the child. As the wife mourns the demise of her daughter, Caroline relocates with the baby to a different state (after informing the doctor), and starts a new life. So far, this is a dramatic (and if one may say so, hard to believe) story. But soon after, the book evolves into a reflective account of the individual journeys of the protagonists: how they face the consequences of the sudden choices made by them over the years, and how people close to them are affected without even being aware of what had transpired in the first place. 

We see Dr. Henry living under the pressure of his choice, and gradually becoming distant from the rest of his family because he cannot communicate with them. While there is an effort on the part of the author to explain to the reader why he made the choice he did, there is an undercurrent of regret, guilt and missed opportunities, an undercurrent that he is consistently aware of. With respect to the relationship with his family, "the lie had grown up between them like a rock, forcing them to grow oddly too, like trees twisting around a boulder." [1] He finds solace in photography and finds recognition as a photographer, hosting art shows all over the world. However, he is painfully aware that photo after photo, he has been trying to "make an image powerful enough to obscure the moment when he turned and handed his daughter to Caroline Gill." [2]

Caroline, on the other hand, patiently raises the child, building a supportive community consisting of her understanding employer, a loving partner and other parents raising children with Down syndrome. She fights the education board of Pennsylvania to get her daughter (and other children like her) a place in the formal education system, witnesses the milestones in her growth and makes arrangements for the time when she would no longer be around to take care of her daughter. What keeps her moving forward is her acceptance that while this was not the life she had imagined or dreamed of, it was "her life, built with care and attention, and it was good." [3]

Based on how the lives of both the protagonists play out, we learn the difference between being imprisoned by a choice versus being nurtured by your choice (and, in turn, nurturing your choice through resilience, love, and community). Dr. Kaushik's "The Real Deal", while belonging to a completely different genre, has plenty to offer with respect to the "nurture/nurturing" aspect of choices. The book, is, of course, about much more. The first half of the book is an account of her experience, struggles, learnings and reflections as a scientist donning multiple hats, while balancing her career and family, especially motherhood. The second half is an exposition of larger issues surrounding science in India, including factors which prevent women scientists from growing into their full potential. Some comprehensive reviews have been written on the book; see, for example, this excellent review by Aditi Jain. 

I have read the first half of the book so far. It speaks straight to the heart on the theme of choices, both in the professional and the personal context. We read the story of a woman who actively makes choices based on her interests and strengths, and works hard to meet the challenges that the choices entail. There are honest accounts of vulnerable moments when she feels she may have hit a wall. For example, she describes the time when she did not hear back from grad schools in her first attempt to apply for a PhD: as a medical doctor with an MD from one of India's most prominent medical institutions, she wondered if her career was over before it started. Through discussions with her spouse, she found a way around this impasse and went on to pursue a PhD. Mr. K encouraged her to volunteer her time at a laboratory in the University of California system, close to where they lived. This would not only give her an experience of the American research ecosystem, but also add strength to her application the next time over. For someone keen on doing a PhD, this was a resourceful and productive way to deal with the situation at hand. As we read the book, we come to learn about several situations beyond her control where a less resourceful person would have given up or descended into cynicism. The book does not shy away from recounting the challenges in pursuing a science career. These include insufficient professional support for young mothers doing a PhD, inadequate resources at state universities, mind-numbing bureaucracy, and incoherent hiring policies at several institutions. But, the undercurrent in this book is that of optimism, openness to opportunities (even when one does not have everything figured out from the word go), and high-agency behaviour.

While reading "The Real Deal", I also got a chance to reflect on another valuable component of "choice-making": learning to make a choice from the point of view of strength rather than a point of view of weakness. We must learn to develop an accurate understanding of our skills, preparation and strengths (professional and otherwise), and keep these at the center of our choices. I observed the protagonist practicing this at many places, and this is among the features that I loved most about the book. She weighed her options and made choices based not only on what an opportunity was offering to her, but also on what she was going to offer to the opportunity. An adequate conviction in our "strong points" gives us the emotional flexibility to consider all angles in our choice, and to be true to our priorities and goals. Choosing and acting from a position of weakness, sadly, does not gain us any brownie points. Instead, it makes us ignore important factors in a choice. It also enables other people to cross boundaries and make unreasonable demands on our time and energy.

Sometimes, our circumstances dictate a certain choice. Sometimes, the choice makes itself. That is, even as we are noting the pros and cons of different options, an event beyond our control leaves us only with one option. Responding to such choices is an exercise in character-building: one tries to find the best way forward while not letting the feeling of victimhood take over our response. On the other hand, in some situations in life, we find ourselves at the crossroads of multiple possibilities, with the freedom to choose the path that suits us best. This is also an exercise in character-building. We learn to balance different parameters of a choice, including our professional training, personal preferences, and family commitments (not necessarily in this order). We learn to discuss, with an open mind, the choice with multiple stakeholders who will be affected by the choice. We learn to seek support for our choices from the right people, and also provide support to them in their choices. We learn to let go of the frustration when a choice does not work out, fully accepting our agency in that choice and also acknowledging that not everything pans out as we thought it would.

I am really glad I redirected my energies from scrolling on social media to reading both these books while reflecting on what goes into making a choice and owning it. Reading these books gave me an opportunity to observe choices from the perspective of those making it. In social media discourse, people judge and question the choices of others on the basis of their own personal needs and desires. But reading well-written books helps us develop the maturity and nuance to view situations from the point of view of people making their own choices. This, in turn, can often generate valuable lessons for ourselves. Can we practice the self-discipline and humility to not burden protagonists with our own voices when reading or hearing about their choices and lives?

[1] Page 258-259, "The Memory Keeper's Daughter" by Kim Edwards, Penguin Books, First Edition, 2005.

[2] Page 274, "The Memory Keeper's Daughter".

[3] Page 253-254, "The Memory Keeper's Daughter".

The teacher's niche

Stepping out of the lecture hall complex at IISER Pune after a class is a veritable treat to the eyes and the attentive mind. Beds of multicoloured flowers around the complex, which keep changing as per the season, help to relax and think about the lecture, what went well, what needs more work and how the course structure is developing. Sometimes, they may also remind one of larger teaching principles. For example, unlike previous years, some of the Gulmohar trees this year have low hanging branches with an abundance of flowers. While looking at one such flower from close quarters, I learnt for the first time that one of the five petals of this flower is larger than the other four, and has a unique layout with yellow and red streaks on a white background. These low hanging branches make one think about how to present a course so that students can get a better glimpse of the underlying beauty. Similarly, while walking past adjacent Tellicherry and the Plumeria trees with their own white flowers blending into each other, an observant passerby cannot help but reflect that any course that we teach is a seamless blend of many areas of mathematics, while also retaining its own unique character.  

This semester, I taught a "topics" course in analytic number theory. This course, not a part of the regular curriculum, introduced students to a wide variety of analytic tools to understand and address some of the most mathematically exciting problems of our times, such as those related to the distribution of primes numbers. The advantage of teaching a topics course is that the students who take such a course genuinely want to explore the content with an open mind. Typically, a topics course is designed and offered by a faculty member who wants to introduce students to areas in which the faculty member works (or in some cases, new areas that they themselves want to learn). Thus, there is a synergy between students who want to learn and an instructor who has a deep desire to teach the subject. Long story short, my teaching duties this semester brought in huge returns on the "job satisfaction" front.  

Number theory is a stream that offers the interested learner a large set of unanswered questions. These questions are easy to state and can often be explained at the level of high school mathematics.  Can we write any even number larger than 2 as a sum of two primes? On a related note, can we write any odd number greater than 5 as a sum of three primes? Can we find infinitely many pairs of consecutive primes with gap 2 such as (3,5), (5,7), (11,13), (17,19) and so on?  For that matter, can we find infinitely many pairs of consecutive primes with gap 4 such as (7,11), (13,17), (1, 23) and so on? This leads to a broader set of questions about the behaviour of gaps between consecutive primes. The "patron saint" of a first course in analytic number theory is a question that was literally asked by a high school student: a 15 year old German boy by the name of Carl Friedrich Gauss who made a guess about the asymptotic growth of prime numbers in 1792. His conjecture was proved more than a 100 years later, and is known as the prime number theorem. The proof came through an article by Bernhard Riemann in 1859 which provided a template and "vision document" to prove the prime number theorem (and more). Riemann described how such questions can be answered by the study of what is now called the Riemann zeta function as a function of complex variables. These ideas were developed into a complete proof of the prime number theorem in 1896 by Hadamard and de la Vallee Poussin independently. Riemann's ideas also provide a framework to address many arithmetic problems of interest in the current times.  Today, "grand unification" themes in mathematics such as the Langlands programme seek to uncover the algebraic structures behind a large class of functions to which Riemann's ideas can be applied.

A typical first course in analytic number theory, aimed at a senior undergraduate student or a beginning postgraduate/PhD student, introduces Riemann's ideas and a complete proof of the prime number theorem along with more refined versions (error terms in the asymptotic distribution of primes) as well as interesting variants such as the distribution of primes in arithmetic progressions (sequences of terms with a constant difference, for example, a sequence with terms 5, 9, 13, 17, 21, 25, 29,....) . Depending on the level of preparation of the students and the goals of the instructor, the course can also aim at developing tools for other problems. For example, to answer questions about writing an even number larger than 2 as a sum of two primes, or any odd number greater than 5 as a sum of three primes, we require the introduction of a method called the circle method. To answer questions about gaps between consecutive primes, we require a set of tools called sieve methods. 

The students taking this course here were in the 3rd or 4th year of the BS-MS programme (the latter equivalent to the first year of a Master's programme), and many had not taken courses that are considered prerequisites for this course, such as complex analysis. At the same time, having taught many of them before, I could count on their enthusiasm and ability to pick up new ideas. So, it felt reasonable to design it like a standard course on this topic for a senior undergrad, keeping the prime number theorem and the mathematics around it as the primary goal. This provided clear learning goals for the course, while also giving us the space to spend time with topics that students had not seen before or were seeing simultaneously with a course in complex analysis. Indeed, extending the Tellicherry and Plumeria analogy, during many classes of our course, a passerby would not have been able to tell whether this was a course on complex analysis or analytic number theory. 

As I mentioned above, a topics course provides a broad canvas for an instructor to introduce students to potential research areas. There were some attendees in the class who had an express intention to work with me. The course gave me an opportunity to introduce them to the kind of problems that I am interested in, without diluting or straying away from the course goals. One of the students, for example, will work on his MS thesis under my guidance. In the last few lectures of the course, we went over the theme of zero-free regions of the Riemann zeta function. When we sat down to go over a preparatory article that he has to read for his project, we noted how the paper felt like a redoing of the course for a different type of zeta function. With the basic analytic framework safely ensconced in his mind, he is well placed to appreciate the new ingredients and challenges that one encounters to study these new functions. Similarly, another student who wants to start his PhD with me, attended the lectures of this course. With foundational preparation in place, once he clears his preliminary requirements for PhD candidacy, we will be able to start working on a new project. 

I love teaching. With every course I teach, I learn a new lesson to improve my teaching practice. Over the years, I have learnt the importance of being organized, properly prepared and of staying true to the course goals, while also leaving space for going beyond them. I have learnt that one earns the trust of genuine students through careful preparation and honest presentation, not hand waving or posturing. I have learnt that we can make mistakes during lectures, and these (mostly) do not cause the world to end. I have learnt that we must accept our mistakes, correct them and move on. I have learnt that practice leads to progress (and fewer mistakes).

Through years of study and research, we develop a "niche". This niche starts reflecting in our teaching. We owe it to the niche to make it reflect clearer and better. And that happens only with time, effort and practice.

Birth, growth, collapse and renewal

Professor Nirmala Jain is a retired professor of Hindi literature from Delhi University, and a well-known literary critic.  A few days ago, after reading her commentary on some well-known Hindi writers (such as Krishna Sobti, Usha Priyamvada and Mannu Bhandari), I was curious to learn more about her own literary journey.  Her autobiography, "Zamane Mein Hum" is a detailed memoir of her life, covering her childhood (she was born in the early 1930s), her long academic career at Delhi University, and her literary associations. I started reading the book in earnest during recent travel, and it gave me an opportunity to reflect on personal resilience in the midst of unrelenting family struggles, the twists and turns of an academic journey, and the joy of being part of an academic ecosystem abundant with talented, purpose-driven scholars. Her journey also provides a glimpse into academically vibrant institutions with great potential devolving into uninspiring workspaces that no longer fulfill that potential. This is the story of many universities in India.

Professor Jain was among the cohort of lecturers who started teaching at Lady Shriram College in the year of its inception, 1956. She spent 14 years at the college. Her interview for the position was chaired by its founder, Lala Shriram, the owner of Delhi Cloth Mills, who also carefully mentored the institution in its early years. She witnessed the change of campus from a small school in Darya Ganj to its current location in Lajpat Nagar with its iconic red building and 55 pillars. She describes the efforts that the faculty members put into the academic training of their students (who came from diverse socio-economic backgrounds) and in creating an atmosphere that fostered wholesome growth encompassing the arts and culture. 

This part of her memoir was fascinating to me for two reasons.  My undergraduate education was completed at Lady Shriram College (LSR).  The college provided a safe, nurturing space for three years to study and reflect on the way forward.  As I entered the college gate every morning after a long, tiring commute from Noida, the red building and its 55 pillars represented a welcoming space that manifested everything positive in my life at that point [0].  A couple of years after graduating, I read the novel "Pachpan Khambein Laal Deewarein" (translation: 55 pillars and red walls) by Usha Priyamvada [1], who was also among the new faculty members who had joined the college. In the world of this novel, however, these pillars and walls symbolized the emotional suffocation of the protagonist. "How could the author not see this space as the intellectually stimulating space that I experienced", my younger self wondered [2]. On the other hand, Professor Jain's narrative was closer to how I viewed the institution, a space that provided its members the resources and opportunities to grow and find their way forward. 

The other reason why I enjoyed reading this part of her story is because it resonated with my experience of starting a faculty position at a new institution.  I joined IISER Kolkata (and later, IISER Pune) in their early years, and saw many transitions of the kind that she describes at LSR.  At a new institution, faculty members have to work with limited resources and often have to take up roles well beyond the purview of the classroom in order to contribute to institution-building [3]. Just as the young Nirmala Jain and her colleagues benefited from mentoring and encouragement by Lala Shriram and other institution builders, we were fortunate to be mentored by inspiring academic leaders such as Professor Ganesh and Professor Shashidhara through tough academic phases (individual as well as institutional). The birth and growth pangs of a new institution intermingled with our personal quest for scientific and intellectual growth.  Reading this part of the memoir revived memories of the journey of the IISERs in the early years. 

The later part of the memoir starts to get sombre. We now start reading stories about the downslide of institutions when a handful of people acquire disproportionate power and start putting themselves above the institution. We read about bureaucratic shenanigans by academics to hurt colleagues who have demonstrated higher scholarly merit, and situations where students try to acquire academic benefits through "extracurricular" means, overlooking the importance of individual, focused effort at the study table. Professor Jain lived through an era which saw the degeneration of many Indian universities into living nightmares. The early phases of this degeneration were also observed by Harivansh Rai Bachchan (a distinguished poet and a professor at Allahabad University who later quit academia) in the third volume of his autobiography. Professor Jain saw institutions in various phases: birth, growth, collapse and renewal. Her memoir presents the story of Delhi University from her point of view. Thanks to her own academic preparation, intellectual curiosity and association with the leading litterateurs of the day, she worked to keep the academic culture of her department alive and thriving. For example, dedicated teachers organized regular conferences and seminars to ensure that students and department members were exposed to distinguished poets and writers who were leading significant literary movements in their times.

The coming up of institutions such as the IISERs, new Central Universities, new IITs and NITs represents a promising phase in science and education in our country (similar to what the older universities represented in the earlier part of the 20th century). The later part of Jain's memoir makes us reflect on what keeps an academic culture flowing and growing versus the attitudes/actions that have the opposite effect. Can we continue with the resolution and clarity of vision to put academic excellence above all else? Can we support and nurture academic potential in ourselves, our colleagues and students? Can we show up every morning to our work with a sense of wonder, and a commitment to give it our best? 

[0] It's a different matter that I had to walk across this part of the building into a darker, less inspiring section where the mathematics classes were conducted.

[1] The pen-name of Professor Usha Saxena-Nilsson, who later worked at Allahabad University and the University of Wisconsin-Madison. 

[2] I learnt to appreciate that no author is obliged to represent something exactly as I view it, even if the topic is close to my heart :-)

[3] For example, folklore has it that Professor Ambika, one of our earliest faculty members at IISER Pune who also served as dean (academics), personally intervened to wake up students who slept late and were at the risk of missing their exams.

Only with time

This semester, I am teaching a batch of students from the 4th year of our Integrated BS-MS programme. Technically, they are at a level equivalent to first year MSc students. Last week, while discussing properties of the Fourier transform with them, I suggested that in case they forget a certain property or formula, but need it, they should not hesitate to work it out by applying the basic definition of a Fourier transform. "Since there's only a handful of you, you will almost certainly get extra time to finish your quiz or exam," I joked. Before I knew it, I started reflecting loudly on an important change that happens gradually in our lives around their age. Up to a certain point in life, academic success almost exclusively depends on how quickly one can answer questions (correctly) in a time-bound exam. But, as we transition into adult life, success or progress in a career (and other parts of life) depends on how much time we are willing to give to a task at hand. 

I was thinking about what my students would be doing in their fifth year and onwards: working on research projects for their MS thesis and beyond. This would involve learning new topics on their own outside of a structured curriculum, often from research papers which are not easy to read. It would involve spending time on answering a new question for which no hints are given at the end of a textbook. There will be no assurance that the answer will arrive, or about when it will arrive. Any progress will be visible after long days and months of tedious calculations and focused thinking on a topic. One will make mistakes, and correct them time and again. The same holds for other areas of our lives: health, fitness, developing personal relationships or learning new skills. A functional adult life is a direct consequence of how much time we devote to whatever we take up (sometimes by choice and sometimes by compulsion), and how patiently we wait for growth or progress.

Many games that we learn in our childhood, such as arranging jigsaw pieces, building objects out of lego pieces and playing chess train us to be generous with time along with concentration. For that matter, even in the exam-dictated part of our lives, the ability to perform well in restricted timelines comes from long hours, days and months of dedicated, unapologetic practice. Thinking or taking quick action on your feet when time is short comes when you have practiced something for long. For example, while learning to play tennis, the backhand motion takes long to learn for many of us (true at least for me). But, a few months of practice down the line, we don't even think for a second when there is a need to use it. Delivering a decent lecture requires a long preparation time. The shorter the lecture time, the longer you have to spend in organizing the essential ideas in order to communicate them without going over time. As Pascal pointed out, even writing short letters takes time. Almost everything meaningful in life requires time and patience. 

Taking time to do something has multiple aspects. The first is the "woodpecker" aspect: the basic "action" level of spending time on activities. This time is to be devoted, either in short, regular chunks of time, or in long chunks, based on the situation. On a regular basis, we set aside time daily for an activity, preferably during hours when there is minimal chance of being disturbed. When a project is stuck or nearing completion, we dedicate larger chunks of time to it, at the cost of ignoring or postponing some other tasks.  During collaborations, things often get sorted out while the collaborators are visiting each other, as opposed to meeting online. While time-bound, regular online (or offline) meetings ensure progress, a collaboration visit nudges all parties to put aside other activities for a while, and spend long hours thinking about something at a stretch. This often accelerates a project out of a rut, and this is precisely why summer time (when we don't have to worry about teaching schedules) is so valuable for scientists. But, in any case, whether in regular periods or in larger, continuous chunks, the woodpecker aspect is about chipping away at something.

The second is the "washing machine" aspect [1]. This aspect is about putting in the time to go through a process. For example, this involves waiting patiently for an experiment to run its course and yield the results. Situations, where we take action, and wait for the consequences, however long it may take. Those of us who waited for visa appointments in the Covid and post-Covid periods will relate to this. There is nothing we can do while the process is going on, other than regular monitoring and paper-work.  The medical treatment to recover from an illness is part of this category. We go through the course of treatment and wait for healing. To a large extent, the endeavour to get fitter could also be considered as an example here. One makes a (hopefully, sustainable) diet and exercise plan, follows it diligently and waits for as long as it takes for the body to respond. 

Then, there is a third "flower blooming" aspect, one of the most important aspects of any scholarly activity. This aspect is about working with a new idea or method, and waiting for time to shape it into different manifestations and applications. Our duty, which is the equivalent of watering and nurturing a plant, is to actively reflect upon the meaning of the idea by thinking about it, making a regular effort to write and rewrite it, and by finding out its connections with other ideas and problems. We try not to let it go unheeded, as we wait for it to "bloom". As an idea blooms, we revisit, polish, review and reframe it over time. As students, this aspect of time comes into play in our journey of learning. While a course introduces a topic, the learning, understanding and absorption of the content will take much longer than a semester and will be each student's individual journey. Here is the translation of a beautiful Sanskrit verse shared by my colleague, Professor Pavan Kumar: "One fourth from the teacher, one fourth from own intelligence, one fourth from classmates, and one fourth only with time".

[1] Most posts on this blog are written during long linen-wash cycles. 

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. 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. 

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 [1]. 

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 [2]? 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 [3]. 

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] 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,

[2] 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. 

[3] 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. 

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.