“Where does math come from?” is likely a far less exciting question than “Where do babies come from?”, but it is one that has been on my mind a lot lately–and for good reasons. As a mathematical researcher, it’s my job to create new math–though whether math is actually created or rather discovered is a question with no easy answer. But as I contemplate my future (hopefully) in a PhD program and reflect on a semester of college teaching, this question becomes even more crucial. I will try to shed some light on it here.
I began thinking seriously about this question a month or so back when working with one of my calculus 1 students. Though a student of video game programming, she was eager to learn why certain math concepts worked the way they did; after all, she was becoming aware that calculus played an important role in computer graphics. Soon we were discussing not only the calculus 1 class material but also concepts from vector calculus and 3D mathematics. It was quite refreshing to have a student so eager not only to understand how to use the concepts but moreover to know where they came from and why they worked–especially a student who was not a pure mathematician. It forced me to think more heavily about how much of our lives hinges on pure mathematics: after all, pure math is the place where math is “born,” where it is brought into the world, tested, proved, and turned into useful tools that can then be applied to engineering and computer science and medicine and so many other of the things that our modern world depends on. And that’s when I decided that this importance could not be kept silent.
I was in the midst of wrangling with grad school applications, applying to several Ph.D. programs around the northeast while trying to figure out what to do about my application to UVM’s Ph.D. program, where pursuing research in pure math seems like a long shot. So I decided to write a letter to UVM’s president, first to thank the math department for the transformative experience I had in the master’s program and then to argue for more support for the pure math side of said department. I made the argument that UVM’s stellar engineering and complex systems program were all dependent on the math created by the pure math program. After a month, a figured I would never hear back, but last week I received a letter from the president saying he was glad to hear I had had such a positive experience in the master’s program and that he was forwarding my concerns to both the dean of the college of engineering and mathematical sciences and the dean of the graduate college. So while I still have no idea what will happen going forward with my Ph.D, I do hope that pure math will get a little more love, and maybe those who come after me will get to see how truly important this subject is.