Hidden deep within the jungle of demands for graduate students is one unspoken, yet clearly important goal: become your own advisor. This painfully mysterious mission was once again apparent in a recent conversation that I had. As is typical when I feel powerless in the machinery of graduate school, I was standing in the library stacks, manically reading the table of contents of any book that looked interesting while repeating the mantra: “That’s fine, I will teach myself.” Searching for books never fails to remind me of why I love math and why I am in graduate school. But after settling on only checking out three books, I was quickly reminded that (for the most part) I am not quite capable of picking up a math book and reading it. Not to mention that checking out three math books is already unreasonable. So, logically, I found a professor I trusted and asked: “How do I find resources that are developmentally appropriate, but allow me to learn the things that I want?” The response: “That’s what an advisor is for.”
Once again, I was reminded that I am powerless. So the real question is, how do we do it? How do we become our own advisors? How do we free ourselves from the shackles of mathematical ignorance and the inability to help ourselves? (Okay, perhaps that last one is a bit much, but it’s a good question.) The best that I can offer is challenge by choice, a method of constantly pushing yourself just a little bit further while acknowledging, yet ultimately postponing, the goals that others are setting for you. As an example, let me explain my (continuing) progression to mathematical independence.
At the start of my first year, the goal set by my professors was clear — attempt to do everything independently. I thought this was great, but a bit out of reach. To give some personal context, I attended a small liberal arts college for my undergraduate degree, where I received a Bachelor’s of Arts in Mathematics, and then taught for three years before deciding to return to school. So even remembering that I want college ruled (not wide ruled!) notebooks was a hurdle to overcome. Hence, I set out to reach the goal of doing everything independently by first doing everything in a group. My initial goal was to read and understand every problem before our group meetings. If I could do that, then I would write ideas for how to prove the problems or maybe even write some solutions (only on scrap paper though, let’s not get too crazy). In the process, I asked a lot of questions like: how do you think about that concept? What made you try those techniques? Why are those two ideas related in your mind? At the beginning, all of these questions were unanswerable, but as the year went on we were able to discuss these processes together. By the end of the first year, my goal was stronger but still mild: write ideas for every problem and argue for valid ideas in group meetings.
During the second year, I continued to push myself. I started by trying all the problems independently and allowing the group to heavily influence modifications. By this, I mean to say that even if I came up with a different solution that we couldn’t find anything wrong with, I was still willing to change to the most commonly accepted solution. Year two ended by meeting only when necessary, handing in solutions apart from the group, following up on problems that I didn’t get correct, and trying unassigned problems. As I continue to work on independence, I am including the goal of communicating math effectively in casual conversation.
So, I offer the method of challenge by choice because you will not only meet goals set by others — you will exceed them. Eventually, you begin to set more tailored and meaningful goals. Fingers crossed, this will lead us to becoming our own advisors.