Today I have some very personal things to talk about. As I mentioned in my last post, I had some things I wanted to talk about regarding what I have been up to in the time I since have taken a break from posting. Today, I am ready to talk about those things.
Back in May, I completed my master’s degree in mathematics at the University of Vermont. YAY! However, for a while it did not seem like much to celebrate at all. I had applied to do my PhD in math here at UVM this past winter, and around the beginning of March I learned that that application was being rejected. I had proposed to study complex systems, an area of applied math in which I had little background. It was not my first choice of work–I had been studying pure math in general and abstract algebra in particular throughout my master’s–but I had been spooked by a reported dearth of funding and advisers in pure math, so, desperate to complete my studies at UVM, I tried to convince myself that I was truly passionate about complex systems. The grad committee wasn’t buying it, though, and that was, as they told me, why my application was rejected.
It was devastating to say the least, not because I was so eager to study complex systems for the next three or more years, but because I had planned my entire life around getting a PhD at UVM. I had a household to support and now was scrambling to find a decent job, and, more importantly, figure out what I was going to do next education-wise, since getting a PhD was still my ultimate goal. In the months since, I have taken care of some practical things: I found a good-paying part-time summer job working as a data analyst at UVM’s Center for Rural Studies, and at the end of this month I will be starting an adjunct teaching job at Champlain College, a small private college right here in Burlington, Vermont. Yet most of all, I have been blessed to have some experiences this summer that have brought my future into sharper focus.
You see, as I believe I have stated several times on this blog, I was the first in my family to go to college. Determined to make my dreams a reality, I poured myself into my studies. I earned a 2200 SAT score, which was no small aid in helping me secure the blessing of a free undergraduate education. As an undergrad, I earned straight A’s nearly every semester and graduated magna cum laude with a double major. I say these things not to brag–certainly many other people have achieved much more–but rather to show that I was accustomed to reaping the benefits of hard work. I began grad school at UVM with the same zeal, but I quickly discovered it to be far more challenging than I had imagined. I certainly wasn’t failing, but I definitely was not having the kind of success I was used to. Afraid to look like I didn’t know what I was doing or did not belong, I withdrew when I should have sought help. I also began to dabble in many different areas of math, hoping to find the ease of success I had always known. Sometimes I did find some success, but other times I found myself knee-deep in material in which I had no background–like complex systems. To make matters worse, I imagined that the other grad students, who all seemed to me to be from vastly different backgrounds than I was, were not having these difficulties. This of course was not necessarily true, but that just goes to show the power of perception. I felt my passion waning.
After graduation, one of the math professors here at UVM gave me an opportunity to work with him on some of his research into the properties of sweep maps, a type of sorting function in combinatorics. I fell in love with the project. As soon as I began studying combinatorics, I instantly connected with it on a deep and intuitive level. The central question of combinatorics–to find how many ways something can be done–seems very concrete and natural, and yet it opens the door to limitless exploration. I quickly became immersed in my research, thinking about it day and night and delighting in the hours I was able to spend with it each day. It felt like working on a giant puzzle, and I gave myself the freedom to play and explore. As I followed my intuition, some of my ideas did not lead to results, but they did lead to new ideas. Soon I was getting results–and asking new questions. And that is when I realized what I had been doing wrong as a master’s student.
I realized that my lack of success–and my lack of enthusiasm–were due to the fact that I was focusing on the wrong things. I had been fixating on getting A’s and “doing it right”–after all, those were the things that had enabled me to get an education in the first place. I was worried about being self-sufficient and not looking incompetent. But all those things are the exact opposite of what being a mathematician is all about. Mathematics is frequently less about getting the “right” answer and more about asking the right questions. After all, you can’t possibly reach a valid conclusion if you don’t start from a valid premise. The work of expanding humankind’s knowledge of mathematics is messy, full of false starts and dead ends that–hopefully, eventually–lead you to the right questions and then the right answers. Collaboration is a must. Once I realized all this, I felt free. And more importantly, I rediscovered the passion that had first led me to mathematics.
Reinvigorated, I am now reapplying to UVM’s PhD program to start in the fall of 2016. I am also applying to several other schools in the Northeastern U.S. I hope to remain at UVM and continue to work on the project I have fallen in love with, but regardless of where I end up, I know that I now have the skills and attitude to successfully complete a PhD program. Most of all, I now have the perspective needed for a successful mathematics career. And I can’t wait to get started.