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 :-)