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.

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.

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.

Two in one

As I have mentioned before, compared to other departments at N1, my department is really short of faculty members.   In the last one year, we somehow managed a mostly one-to-one mapping between our courses and instructors per semester, with some of us teaching two courses [one course typically being a higher level course taught to students in upper years ].   However, in the new course structure, we will be teaching two extra courses per semester from next year.  We further wish to strengthen our Integrated Master's and PhD programme and add some more courses to it instead if asking these students to take courses with upper year undergraduates.

Combine this with the dwindling number of faculty members in our department and you have a situation in which we will all need to teach two courses per semester.
As I was describing this situation to a colleague from a very well-endowed department, he remarked, "two courses per semester? That's a fate I wouldn't wish for my enemies!"

I appreciate this colleague's concern for my department.  Most of my own departmental colleagues have also thought about it.  Given that most of us are very young and building up our research programmes, we would ideally like a teaching load of at most one course per semester, just like our friends in the other departments.  Nonetheless, we are mentally prepared for this scenario [0].

A colleague, who has been instrumental in designing our courses and has taught multiple courses per semester before, feels that it will not be as difficult as we have ourselves designed our course structure and content.  Contributing to a scheme which we feel strongly about will be challenging and will not feel like a burden.  I share my colleague's optimism, but am also aware of the challenges of multi-teaching.

In the previous semester, I taught two courses for the first time.   Both were taught to moderately sized groups.  I had very ambitious plans for both these courses.  I wanted to upload typed course notes for both of them because typing things out makes the structure and material very clear in my mind.  The plan was to prepare all lectures for course 1 in the coming week on Saturday, lectures for course 2 on Sunday and spend about one and a half hours each daily typing up the notes during the weekdays.  This, as I foresaw, would also give me ample time for research.

As it turned out, however, I found preparing the lectures much more challenging and time consuming than I had thought.  It would take me the entire weekend to prepare the lectures of one course (the course which I had thought would be easier to teach!)  I would prepare the lectures for course 2 during the weekdays and this also took a lot of time.  So, I toned down my ambitious plans and was able to put up typed notes only for one course till the middle of the semester.  After that, as the pace of the lectures increased, the time spent in preparing them increased even more and I had to give up typing notes for good.  I also found myself not able to give as much time to my PhD and Master's student as I would have liked.

Perhaps, teaching both these courses could have been less strenuous if I had taught at least one of them before.  With more experience, pursuing this kind of teaching load without impacting research work can also possibly become "second" nature.  But, as of now, it certainly is a challenge and entails very strict time management.

In the coming semester, I will be teaching two courses.  I have already taught one of them before and have the course notes ready [1].  So, this semester will be an opportunity to upgrade the material and the presentation [2].  The second course will be taken by a Master's student and Integrated PhD student doing projects with me and I have already planned for it according to their requirement.  As an additional advantage, this will add to the time I can devote to them.  If one has to teach two courses in one semester, this is the optimal course allotment one can hope for and we would want to ensure a similar arrangement for all department instructors as much as possible.

In my field, teaching two courses per semester is very common in similar Indian institutes as well as in North American universities.  Postdocs and PhD students might have it easier with just one course per semester, but permanent faculty, in a large number of research universities, have a 2:1 or 2:2 course load.  Faculty members at places with a 1:1 load consider themselves lucky to have a light load.

Here, however, almost all my colleagues have graduated from institutes where 1:0 load is more of a norm (if not 0:0!)  Most had not taught before joining N1.  So, a 2:2 or 2:1 load seems daunting because one is simply not habituated to it.

I look forward to hearing from readers about their current teaching loads, their thoughts about it and the load they would ideally like to have.


[0] I am writing this post under the assumption that there are two teaching semesters - autumn and spring.  The summer months are non-teaching months.  Some senior professors at the institute have floated the idea of offering "soft" courses in the summer semester, but at the moment, I don't want to go in there!


[1] I was supposed to teach a first year course before, but recent changes in the course structure and our departmental composition have necessitated  the outsourcing of this course to a colleague from another department.


[2] Teaching the same course over and over again can become boring and uninspiring.

Intelligent course designing

Recently, there has been much introspection at N1 about its undergraduate programme.  The first two batches of our undergraduate programme have done very well and most have got into prestigious PhD programmes all over the world.
While there is much appreciation of this fact, it is also felt that in the current course structure, the performance of students in the first two years has not been up to the mark.

Naturally, some are questioning whether our current process of admitting students, in the quest to fill up the number of seats specified by MHRD, is compromising on the quality of students.  This question assumes special importance in the current national debate concerning the IIT entrance exams.

The other question that people are asking is whether the current course structure of our undergraduate programme is the best structure to provide a strong foundation to our students in the sciences?  Is this system optimal from the point of view of the students? Has this system been fair to the students that we do get? Can we make our programme more accessible to our students without diluting our courses and without compromising on the objectives of our institute?

In the current system, students take a broad variety of courses in the sciences in the first two years  and choose a major subject in the third year (though they also continue to study interdisciplinary courses).  Thus, in the first two years, the students have to learn enough about different sciences to be able to develop a broad perspective in science and make an informed choice of their major.  The primary challenges in this system are

a) the jump from class twelfth to the first year of this programme.  Since each discipline is only represented by one course per semester for the first four semesters, a lot of material needs to be covered to prepare the students for the intensive courses that they take in the third year.  Many students are unable to handle the pressure at this early stage.  For example, students who opted for Biology in 11th and 12th now have a hard time keeping up with their peers in their first year Mathematics course (and vice versa).

b) Once a student decides to major in a subject A in the third year, she again has to make a big jump from what she studied in A in the first two years and the advanced material that she sees now in the third year.  Does one course of A each semester in the first four semesters adequately prepare the student to make an informed decision about choosing A as a major and then undertake five intensive courses of A each semester in the third year?  Keeping this in mind, when instructors try to ensure that students in the first two years have the necessary pre-requisites for year 3 by following a challenging course syllabus, many students experience burn-out.


There was some serious rethinking about these matters from the course-structure point of view rather than the quality-of-student point of view and various remedies were suggested.  Somewhere between the extreme of narrowing down a student to one subject in the first year itself and that of making all courses "gentle" was found the right balance.  Basically, the incline from one year to another has been made more gradual.

As per the new structure, which has now been approved by the senate,
a) Just as before, students will take one course per semester in each of the sciences in the first year.
b) In the second year, students will now choose three sciences of their interest and take three courses per semester in each of the chosen subjects.   These courses will be more rigorous than the first year courses.
c) In the third year, the student will choose a major from among the three subjects chosen in the second year.

The new structure has generated enthusiasm among many faculty members.  We feel that it gives us more space to introduce the most fundamental aspects of our fields in the first two years in a way that students have enough time to follow and digest what is being taught to them.  

Each department now has the fundamental task of redesigning the first year course and introducing appropriate new courses in the second year.  The next couple of weeks will be spent doing this as the new plan will be put into action in the coming semester.

I would like to hear from readers about the undergraduate course structures at their institutes in the initial years and their thoughts about it, either as a student or instructor (or both).

Generation gap?

Like many other new institutes, the faculty at N1 almost entirely consists of young members within five to ten years of their PhD.  The associate professors (few) and full professors (fewer) can be counted on fingertips.  Our senior colleagues have substantially contributed to the growth of N1 and by their accomplishments and experience, have been able to give direction to the institute.  What I also admire about them is that they left good positions in established institutes and roughed it out in a new set up and at the same time, managed to keep their research programmes going.  Their commitment and leadership is deeply appreciated.

Sometimes, however, there is a bit of a gap in communication between the younger faculty (YF) and senior faculty (SF) members.  I would like to share an example of how something said by YF can be misinterpreted by SF and vice versa.

A lot of heated conversations are centered around the balance between teaching and research.  On joining, the message that most of us get is that while there should be no compromises in teaching undergraduate courses in our flagship programme, eventually our performance will be judged on the basis of our publications and research grants.  Those of us who did their PhD/postdocs in North American universities have had prior teaching experience and have also seen our supervisors/postdoc guides balancing and actively performing both duties.  On the other hand, many of my colleagues have joined after doing postdocs in research institutes in India and Europe.  Thus, they may not have had any teaching experience prior to joining here and have come out of a system where undergraduate education was not given much priority.

Faced with the challenges of teaching their first course and trying to carve out an independent identity in the research world simultaneously, some YFs are occasionally heard saying that their teaching duties take time away from their research work.  I would not doubt  the commitment of a colleague who says this towards teaching well.  I would only think that my colleague is dealing with time management issues, an important part of the learning curve of any faculty member and is frankly sharing his/her struggles with others.

Unfortunately, however, if our SFs hear this, more often than not, they will angrily retort and say that they had much heavier teaching loads when they started out and that YF has it much easier and therefore should not complain.  SF might even make a general statement on the lines of ``People should not make teaching an excuse for their lack of productivity."  Perhaps, SF is making a general statement, but YF will be stunned because s/he has been very productive.  Needless to say, this conversation may not end very well.

SF's reaction is based on the assumption that YF was making teaching load an excuse for weakness, where as all YF was doing was harmlessly interacting with colleagues and sharing his/her struggles.  On the other hand, even though SF made an off-hand general remark, it is next to impossible for YF to not take it personally!  Perhaps, it might have been better if SF too had shared some stories of their early career days or given some advice. While it is considered impolite to offer unsolicited advice, surely unsolicited advice is better than unsolicited criticism?

Teaching was only one example.  Similar conversations can also happen around other issues like research facilities, lab/office space, personal facilities like transport, housing etc.

On a personal note, I often don't mind when a senior says things like ``I had it much harder," provided the senior gives a concrete example and describes how s/he handled it.  I get this a lot from my father and it usually has the desired effect.
When I was describing the above situation to him the other day, his reply was:

`` In army, a junior will not dare to open his mouth when a senior is talking.  You academic people have it much easier."

I will leave it to the readers to agree or disagree with my father :)