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.