Every now and then, an opportunity hits my inbox. A possible internship, project, service activity, you name it. One September day, I got an email about a math education research position for a graduate student at the University of Tennessee (my current academic home). A faculty member wanted some help with a project for developing math curricula for middle school students. While I don’t remember the exact details about this project, I asked my research advisors about it, and they strongly discouraged me from taking it on.

Why? Well, I had indicated to them previously that I wanted to pursue a postdoctoral research position after graduating. They said that a project of this nature would not enhance my application for such a position; if instead I wanted to work at a liberal arts college, for instance, then the project would have been a great idea. To them, it was a matter of focus: focus on the things that will help me get the job I want. Anything related to math research (not math education) they seem perfectly OK with me pursuing, and have openly encouraged me to do as such.What does that conversation have to do with winter break if it took place a few months ago? Well, it influenced how I spent my winter break: sure I relaxed, but I felt the need to keep busy so I wouldn’t get bored out of my mind. Rather than wander around aimlessly on a bunch of random projects, I worked almost exclusively on my thesis. While there was one specific task my advisors wanted me to work on, I spent a week getting as far along on that as I could on my own, and then went ahead and finished up/addressed several other parts of the project that were hanging over my head. Having them all sitting in my head for a long time gradually helped me figure them out, because they were all related to each other.

Since I’ve worked on this project for about a year and a half, I’ve started getting well acquainted with the research landscape in my particular area of specialty. In particular, I’m now more familiar with the tools used to solve related problems, and now have a fairly large collection of things I can show my advisors. Not only was the winter break “precious” time where I could work on research without worrying about coursework or teaching responsibilities, but it gave me a chance to prove that I have some semblance of autonomy. This is important to me because one of the big goals of a Ph.D. program is to train an individual to perform original research independently, and I’ve got to start somewhere. While I still rely on my advisors for some guidance, I want to at the least build some competency in figuring out the details of delicate technical arguments by myself. If I can do this, then I can spend more of my meeting time with my advisors discussing bigger-picture proof strategies and ideas for how to advance the project (from both a theoretical and a computational perspective).