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.
我的一些朋友追求校园的其他专业没有“资格”以写论文。他们所要做的就是表达兴趣，他们可以开始写作。对我来说，这是关于该领域的排他性的进一步陈述：数学是一种严谨的纪律，我们必须限制对最顶级学生的访问。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.
我尽我所能忘记考试经验，并迈出前进，享受我的其他数学专业。然而，我的高级要求我花了一段时间考虑大学毕业后做的事情。我寻求家人，朋友和教师的建议。我的家庭建议我追求工程，因为我可以获得可靠和高薪的工作，而我的一位朋友建议精算工作，因为这就是他计划的工作。所有这些想法都听起来很实际，但我在内心深处，我的激情是继续学习理论数学。当我用我的拓扑教授讨论未来时，他说他认为我会成为一位伟大的老师。当然，他暗示我教高中。虽然这是一个恭维，但它刺痛了一点点，因为通过他的话，我听说我在大学水平教学不够好，这是我的秘密野心。我没有与任何人分享秘密雄心壮志，因为害怕有人会直接对我说话：Graduate school in mathematics is for the best and the brightest. You haven’t proved yourself to be in this group.
我很高兴回到教室里 - 无论是一名学生还是老师。能够在微积分序列中教授所有课程真是太棒了。它加强了我对这个主题的了解，它给了我一些有用的经历，当我申请工作时帮助了很多。在研究生院，我拿走了一位女教授所教导的第一个也是唯一的课程，这很棒。谁知道？如果她留下来，我可能已经进入了抽象的代数。幸运的是，我周围还有其他非常支持的教师，我发现了一个拥有一个美妙的真实分析师的家园。
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.
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.