(Second week of the Fall semester. Tuesday morning, 8:30am.)
I am in my office in the Mathematics building at 111 Cummington Street, on the Boston University campus, fidgeting while I go over my notes for the n-th time, just a few minutes before my very first class. As a teaching assistant (TA), I am only responsible for discussion sections (with about 20 students in each section), but I am seriously nervous nonetheless. After all, it is the very first time I will be in front of a classroom.
– Can I do this? – I ask myself, and I simply do not know the answer to my own question. My career as a mathematician seems to hinge on this moment. What if I just cannot do it? What if I am a terrible instructor? What if it is a miserable experience, either for the students, or for me, or worse, for all of us? I have always loved doing math, I love talking about math, I am excited about the concept of teaching math to others, but I have little to no experience speaking in public, and I am gripped by fear. During my college years (in Madrid, Spain), I would rarely participate out loud during a lecture, and I would even have a hard time approaching an instructor after class to ask a question. I would choke on the words, stutter, imperceptibly shake and, as an unfortunate result, I would avoid engaging with most of my professors, unless strictly necessary. All those interactions in college, had they happened, would have been in Spanish, in my native tongue, so my fears today are compounded since, of course, I have to run my discussion sections in English. What if the words do not come to me? What if the students do not understand me? What if they complain about (or mock) my accent?
This is the beginning of my second year at BU. Thanks to a scholarship, I did not have to teach during my first year, which allowed me to concentrate on my graduate courses, on passing the preliminary exams and, at the same time, improve my English skills, both written and spoken. My language (and mathematical) skills have indeed significantly improved, so that makes me feel slightly more confident about being in front of a class of students, but when I am nervous, my English speaking ability regresses and noticeably deteriorates. And today, I am very nervous.
To add insult to injury, the end of the summer and the beginning of the Fall semester have been quite hectic, reaching overwhelming levels, for several reasons which were, briefly and in chronological order: trip to Spain that had to be short, attended a teaching orientation, fell in love, moved out from my apartment and moved into a house with some friends, started taking some advanced courses, met for the first time with my potential thesis advisor.
(Week before Fall classes start.)
After my first year living in the USA, I flew back to Spain to visit my family, but it was a relatively short trip, as I had to get back for a TA training during the week before classes start. Given my anxiety about my impending teaching debut, I was in fact looking forward to the TA orientation, in hopes that there would be some illuminating moments, helpful tips, or instructional wisdom that would allow me to conquer my stage fright. Back then, the TA orientation at BU was a day-long event that began with back-to-back presentations from different representatives from various administrative offices on campus. I barely recall the content of the anodyne presentations, except for the fact that almost every presenter emphasized one point above all others: do not date your students!
When the first part concluded, the graduate students were herded to an outdoors lunch, at a quaint little lawn, behind to the BU Chapel, near the so-called BU Beach. After grabbing some food, my fellow math graduate students congregated into a small group, the older students introduced themselves to the first year students and, together, we summarized the morning session: the consensus was that all the information and talks we heard in the first half of the day were completely useless for a TA in mathematics. The people in our small circle were chatting and joking about absolutely not dating students but I tuned them out, as I was soon day dreaming, for I had just met Marisa for the first time. She was a first year masters student, who had just arrived from New York city where she had worked as a consultant, and was here, back to school, to get a masters degree in computational mathematics that would make her competitive for her dream job: a company that applied mathematics to environmental modeling. I was immediately fascinated by everything about Marisa: her passion, her determination, her real-life experience, her smile. Neither one of us could possibly fathom that in a few months we would start dating (shortly after a Halloween party at my house), that we would get married a few years later, that we would move to Maine, then to New York, to Connecticut, and back to Massachusetts, that we would make friends and laugh and cry and enjoy life and suffer together, and that we would eventually settle down, buy a house, and have two beautiful kids. For the time being, taking things one step at a time, I just tried to not make a fool of myself in her presence during lunch time.
The second part of the orientation day was only slightly more useful. We were subdivided into smaller groups, and we were sent to classrooms to perform a teaching sample in front of an audience formed by a session leader and our fellow TAs in training. Each one of us was supposed to prepare a 5-minute mini-lesson on a topic in our area. A usual challenge for a mathematician is to choose a topic for an audience of grad students in various research areas, from the humanities to the sciences: I decided on a short explanation on how to complete a square and apply it to solving a quadratic equation, and patiently waited for my turn to present. After witnessing a few of the sample lessons from other students, I was horrified that some of these people would be teaching students the following week. And this only made me more nervous as I thought that, surely, I may be just as bad.
Finally, after much waiting, and much build up of anticipation, it was my turn to speak. I gave my little lesson, as best I could, and waited for the room’s combined wisdom, comments, insights, thoughts, remarks, suggestions, and constructive criticism that would help me become a decent instructor.
– Good! – the session leader said, and after a cursory look around to verify that no one could top such brilliant feedback, he continued – Next! – and that was that.
(Weekend before Fall classes start.)
As I had been warned and as I found out myself, September 1st, also known as Boston moving day, is the most chaotic day of the year in the Boston area since, it would seem, the entire city’s population swaps apartments, packing one, moving furniture in any available vehicle, and unpacking all the belongings in the new living space. Most of those people moving are one of the many undergraduate and graduate students living in the area.
My own move from an apartment in Brookline to a house in North Brighton was stressful, as expected, but largely uneventful. My new roommates were a couple of other fellow math grad students (one in algebra/number theory like me, another one in dynamics), and two of their friends, who were not math related, and they already had real-life jobs. Living with friends was a completely new experience for me, because I lived with my parents as an undergrad in Madrid, but I was quite happy with the arrangement. Since I barely had any belongings (a bed, a shelf, a few books, a stereo system, a large suitcase worth of clothes), the room I picked was the smallest in the house and my rent was, by far, the lowest of all the housemates. My room was indeed so small, that it may very well have been a walk-in closet for my roommate Caleb’s bedroom. However, I did not mind the somewhat spartan living, and the lower rent would allow me to save some money for my flights to Spain and other various trips in North America, and I would be able to buy a few math books that I had my eyes on for a while.
(First week of Fall classes.)
Boston moving day was a Saturday, Labor Day was on Monday, and classes started on a Tuesday. Discussion sections, however, did not start until the second week of classes, so I had a week to get started with my own course load: algebraic geometry, algebraic topology, and a directed study in number theory. The latter was a reading course with David Rohrlich, on the topic of elliptic curves. This was my first step in the song and dance that is choosing a thesis advisor, and a thesis topic, so I spent many hours in the library reading Silverman’s beautiful textbook ahead of our first meeting, and consulting other references for the necessary background. The first meeting went very smoothly, as we just went over the contents of the book and sketched a plan for the semester, so I knew what sections I had to prepare to present each week. Rohrlich was, since day one, extremely gentle and polite, understanding and encouraging, which made the decision (on my part) of choosing an advisor one of the easiest of my life but, regardless, that is the topic of a different story.
In addition to attending my own graduate courses, I was advised by the Calculus instructor I was working with to attend the main lecture during the first week, to get an idea of the pace and level of the material we were supposed to cover. Glad to do so, I went to the professor’s lectures, and she graciously introduced me to the class, so they all could recognize the face of the poor soul that would be trying to help them through their personal freshman Calculus hell.
(Second week of the Fall semester. Tuesday morning, 8:55am.)
I am walking down a sterile hallway in the basement of the Mathematics building towards a classroom, about to teach my very first class. In an attempt to remain calm, I breath deeply and in regular intervals, but it is not helping. Just to keep me busy, a mental list of things that I need to go over with the students when the class starts keeps circling in my head. When I reach the room, a few students are already waiting and they observe me with curiosity as I approach the desk at the front of the classroom. A couple of students in the back whisper some comments to each other. On the blackboard, I write down my name, my office number, my email address, and my chosen office hours. There are still a couple of minutes left to kill before class starts, so I just scan the room, and mentally count how many students are already in it, while I try to match faces to the names in my printed class list, to no use. I quickly go over my notes for the hundredth time this morning, and look impatiently at my watch, until the time is precisely 9am.
One last deep breath, and I start the class – Hello everyone! – and, immediately, I have the certainty that everything is going to be ok. Not because my nerves are gone (they aren’t), but because the students seem more nervous than I am, and that is strangely comforting and reassuring. I begin the script that I have prepared and, to my relief, I am quickly easing into it. This is my name, this is how you pronounce it, here is my contact info, let us learn a bit more about you. I let them introduce themselves, I ask them to tell me something fun they did during the summer, and I repeat their names a few times, trying to get the pronunciation up to some standard they are comfortable enough with, until they let me move on to the next person. I draw a small checkmark next to their names in my printout and notice that a few students are missing. This reminds me to tell them that there will be quizzes at the end of each section (except today), and I categorically assert that there will be no make-up quizzes unless a catastrophe happens, or there is a justifiable medical excuse, words that I will regret for the rest of my life. Once the introductions are over, I tell them a bit more about what I intend to do during discussion sections, and I encourage them to bring questions to class that we can solve together. And without further ado, we start reviewing some material from the previous week, and solving as many prototypical exercises as time allows.
(Second week of the Fall semester. Tuesday morning, 9:50am.)
Before I realize it, time is up, and the 50 alloted minutes have elapsed. I am surprised how fast time went by, and start packing my things, when a few students come up to me to ask me various logistical questions about exams and certain absences due to university-sanctioned events. I do not have an answer at my fingertips, but I promise I will get back to them once I check with the main lecture instructor.
As I walk out of the room, I am elated that class went much better than I could have imagined and, in fact, it was truly enjoyable. Some students seemed inert, following my examples with dead eyes, but a few of their classmates followed along with interest, and even answered some of my questions. Thus, I am ready to declare the first class a resounding success. As I am walking upstairs from the basement level, I cannot wait to share the good news with some of my fellow graduate students, and I notice that Marisa is coming my way, so I am quickly calculating some words to share my elation with her, when I realize that she is upset and crying. She runs past me, going upstairs, and I do not have enough time to even finish my – is everything ok? – before she is gone. My happiness is instantly erased with the premonition that something is indeed horribly wrong.
I walk towards the main office, and the silence in the hallway is unusual and eerie. A sound, out of place, starts to form as I approach the staff offices, until I am able to recognize it as the voices of newscasters, coming out of a television set. Someone has rolled out a cart into the waiting area by the Chair’s office, and a TV set is on top of the cart. A few staff, faculty, the Chair, and students have gathered around the TV, and are intently watching in silence the images on the screen. A chill rolls down my spine, as I advance toward the TV and notice that a few people are sobbing, just like Marisa was. – What happened? – I ask, but no one responds. They just keep watching the screen and invite me to try to understand the images myself, for the scene is incomprehensible and impossible to explain in a few words. Both towers of the World Trade Center in New York City are on fire, and thick plumes of smoke rise above them. I am about to formulate another question, trying to understand why both towers are on fire, when they repeat a previous recording of a large plane, Flight 175, crashing into Tower 2 of the WTC, followed by a huge explosion. I am trying to process this haunting image, when they cut to a live feed as, at 9:59am, the same tower collapses. A few of us gasp in horror and I join in the sobbing as tears roll down my face.
It finally dawns on me that my parents might be watching the same images on the other side of the Atlantic ocean, and are probably scared out of their minds for my well-being. I run as fast as I can out of the building, across the street, towards a payphone situated next to McDonalds. Since I do not have enough change, I collect-call Spain, and my mother answers the phone. As I had correctly surmised, my parents are extremely relieved to hear my voice, even if I do not live in NYC. I have no comforting details or explanations to offer (no one does) and all I can say is that I am perfectly fine, just shaken and confused. In fact, I am afraid, but I would not tell that to my parents on the phone. I hang up and go back to the Math main office, only to find out that the situation has exponentially worsened with the collapse of Tower 1, while the Pentagon is now reportedly on fire, and another plane has crashed somewhere in Pennsylvania. The newscasters are starting to estimate a possible death toll, and the room starts spinning around me. Finding myself physically ill, I go to my office and I follow the rest of the news from there, as the nightmare unfolds.
(September, 2001.)
The worst terrorist attack imaginable was perpetrated while I was teaching my first class. Practically everyone was traumatized by the horror in one way or another, because they had a friend, a family member, a loved one, or a former coworker directly affected by the attacks, or simply because they saw the images over and over in disbelief. Many of our students were touched by tragedy, at a personal and/or psychological level, and instructors and TAs made as many accommodations, homework extensions, and makeup exams and quizzes as necessary.
I will be forever mortified by my choice of words (unless a catastrophe happens) on that day. The whole situation also made me deeply ashamed of the fact that I had been so self-centered for the previous several months. My worries about moving, teaching, my accent, research, seemed so trivial and petty all of a sudden, dwarfed when compared to the magnitude of what was happening a few hundred miles away, and the impending wars in Iraq and Afghanistan. The attacks also made me open my eyes and reflect on how friendly and welcoming the USA and their people had been to me, and thinking about all that took place made me suffer in agony for all those personally affected by tragedy.
Teaching still made me nervous, but I learned to put things in a sobering perspective. As a matter of fact, I am still nervous about teaching today, but I have come to embrace it is a positive thing. It means that I care, and as long as I am nervous before a class, I know that I will take the time to prepare adequately and do a good job in the classroom.
A Field Guide to Mathematics 
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