I almost ended my study of mathematics after my bachelor’s degree. I am now grateful for the series of circumstances and decisions that led me to graduate school in mathematics, and ultimately to a fulfilling career at a school that is a perfect fit for me. Knowing how happy I am now, it would have been a shame had I given up on this dream.
I fell in love with mathematics during my college years. I was fortunate to attend a top-rated liberal arts college and to take classes with professors who were truly gifted at their craft. I enjoyed my classes and worked hard, but I was not a straight ‘A’ student; perhaps I was a “late bloomer”. I finally took Linear Algebra as a junior, and discovered that I loved writing proofs. What’s more—my professor noticed my interest, he saw potential in me, and he encouraged me to continue asking questions. My confidence was at an all-time high.
I began to wonder if I would like to go to graduate school in mathematics. It sounded both terrifying and delightful at the same time. But would my B+ average in my major be enough to get me into graduate school? I wasn’t sure. I soon learned that the department offered the opportunity to write an honors thesis in mathematics. Surely, this was something that I should pursue, because it would help me to decide whether graduate school was for me. In order to write a thesis, I had to complete a qualifying exam in the spring of my junior year. The exam consisted of three parts. The first part tested one’s knowledge of the ‘core’ subjects: Calculus 1, 2, and 3, and Linear Algebra. Each student was then able to choose two additional subjects in which to be tested. I chose Real Analysis and Combinatorics, since I had recently completed those courses. This was the same exam that seniors faced in order to earn their degree in mathematics. Seniors were required to earn a ‘pass’ on all three parts of the exam. Juniors wanting to qualify to write a thesis would need to earn a ‘high pass’ on all parts of the exam. I would have two attempts at the exam.
Some of my friends pursuing other majors on campus did not have to ‘qualify’ in order to write a thesis. All they had to do was express an interest, and they could begin writing. To me, this was a further statement about the exclusivity of the field: mathematics is such a rigorous discipline that we must restrict access to the very top students. Students who undertook the challenge of a thesis would have a chance to graduate with Latin honors. I couldn’t care less about graduating with honors, but I very much wanted the experience of writing a thesis! So, I spent my winter break studying intensely in hopes of doing well on the exams.
Sadly, I was not able to earn the three scores of ‘high pass’ that were needed to qualify to write a thesis. I think I earned two grades of ‘high pass,’ and on one part of the exam I simply earned a ‘pass’. On my second attempt, it was the same thing, only a different part of the exam tripped me up. I was devastated. Couldn’t the faculty see my passion for mathematics? Didn’t that count for anything? At that point, I felt that I should abandon any hope of going to graduate school. I was not among the best and the brightest. I was not good enough. While the fall semester of my junior year had boosted my confidence, by the end of the year my confidence was gone.
I did my best to forget the exam experience and to just move forward and enjoy the rest of my mathematics major. My senior year, however, required that I spend some time thinking about what to do after college. I sought the advice of family, friends, and faculty. My family suggested that I pursue engineering because I could get a reliable and high-paying job, and a friend of mine suggested actuarial work because that was what he planned to do. All of these ideas sounded practical, but I knew deep inside that my passion was to continue studying theoretical mathematics. When I discussed the future with my Topology professor, he said that he thought that I would be a great teacher. Of course, he was suggesting that I teach high school. While this was intended as a compliment, it stung a little bit, because through his words I could hear that I was not good enough for teaching at the college level, which was my secret ambition. I didn’t share my secret ambition with anyone, for fear that someone would say the words directly to me: Graduate school in mathematics is for the best and the brightest. You haven’t proved yourself to be in this group.
I convinced myself that teaching high school would be fun, and I would still get to interact with mathematics. I entered a graduate program where I would be teaching at a public high school and earning an M.Ed. and teacher certification at the same time. While I enjoyed the teaching, I missed the challenging and fun math classes that had made me feel so invigorated in college. One day as I was lamenting this, I came to the realization that there was nothing stopping me from continuing my studies. Maybe I hadn’t been a straight ‘A’ student, and maybe I didn’t write an undergraduate thesis, but I was willing to work hard and I was passionate about mathematics. I mustered some confidence, sent in a few applications, and crossed my fingers. I was thrilled when I was admitted to graduate school with a teaching assistantship to help pay my way.
I was so happy to be back in the classroom—both as a student and as a teacher. Being able to teach all of the courses in the calculus sequence was awesome. It reinforced my knowledge of the subject and it gave me some useful experience which helped a lot when I was applying for jobs. In graduate school, I took my first and only course that was taught by a female professor, and it was wonderful. Who knows? I might have gone into abstract algebra if she had stayed around. Fortunately, there were other very supportive faculty around me, and I found a home working with a wonderful real analyst.
Of course, things got more challenging as I worked on a thesis and struggled to obtain results. I thought about quitting more than once, because it was so easy to get discouraged when the results weren’t coming quickly enough. It did not help to see three friends of mine—all women—leave the Ph.D. program before completing their degrees. By that point, however, I knew the exact career that I was after. I wanted to be a professor at a small college – I felt that I would be good at it, and that is what got me through the tough times in graduate school. I kept my eye on the prize.
The disappointment that I faced in my undergraduate years haunted me for way too long, but once I had a good job I was able to put it behind me and focus on my career. I can now say that not writing an undergraduate thesis was probably for the best. Perhaps I was not fully prepared for what it entailed. Perhaps I would have done a poor job and become even more discouraged. Or maybe I would have rocked it! I will never know. The experience definitely woke me up to the reality that there would be other challenges in the future—qualifying exams, a thesis defense, job interviews, a tenure decision. We are always being evaluated by others, and it is very difficult to get away from that. The key is to stay true to yourself and not worry too much about what others think of you. Unfortunately, most of us don’t come to this realization until we are more settled in our lives and careers.
I am proud of my resilience throughout all of the challenging times—especially when I viewed those exam results as a sign that I was not good enough for graduate school. I had to put aside my past failures and my concerns about how others viewed me, and just go after what I wanted. I knew that if I didn’t try for the Ph.D., I would always wonder about what might have been. Once I realized this, I knew that I couldn’t move forward along any other path if I was always dreaming of being a mathematics professor. There was nothing to do but to continue on my mathematical journey.
Historically, the doors to the field of mathematics have not been wide open to all, but I have hope that this attitude is changing. My experiences have taught me the following: as a teacher, my words mean so much to a young, impressionable student. My encouragement, or lack thereof, is visible to others. Moreover, noticing someone’s interest is as important as recognizing their talent and hard work. I hope to do my best to welcome my students into mathematics so that they can enjoy it as much as I do. While it is tempting to be “realistic” when they struggle in my classes, I hope to remember to not give up too easily in nurturing their passion for the field.
For the past 25 years, Pamela Pierce has been teaching at The College of Wooster, where every student writes a senior thesis. She earned her bachelor’s degree from Amherst College, her M.Ed. from the University of Massachusetts, and her M.S. and Ph.D. degrees in mathematics from Syracuse University. She has been inspired by many of her mathematics professors, but especially by Dan Waterman, her thesis advisor at Syracuse. Pam works in the field of real analysis and is active in the Summer Symposium in Real Analysis, which she has hosted twice. In 2009, she won the Trevor Evans Award from the MAA, and she is currently serving on the editorial board of Math Horizons. In her spare time, Pam enjoys music, traveling, and swimming.