The last few years have been humbling experiences. I’ve been coming to terms with who I am and who I want to be, fortunately they’re not too different.
A few years ago I prepared for my comprehensive exams in physics. I pored over old exams that dated back more than a decade. While there were questions that repeated, the format seemed wide open. Nearly anything (appropriate for the level of my department) could be asked. How was I going to remember all these different problems? It’s easy while you’re taking courses to have tunnel vision. Faculty generally encourage it by assigning problems from specific chapters of specific books with implicit assumptions about whether we should be thinking relativistic or quantum mechanical.
I threw away all the old exams. What was the point of looking at problems? I didn’t know what problems were going to be on the exam. I didn’t know if I would be able to solve the problems. If the exams were any good I wouldn’t have seen the problems before anyway. I spent a month (it’s all I had) organizing my understanding of physics. I used concept diagrams, took up whole blackboards trying to tie together different results, when they held, what they meant and what they implied. I organized my knowledge and the only real computations I did was to review some basic techniques.
I can’t avoid making this post sound dramatic, but that month was like an academic vision quest. I realized how little I had learned as an undergrad and a graduate student. I had earned good marks, but I had earned those marks working problems from specific chapters in specific classes. That month was a wonderful synthesis of ideas and I felt ready for the exams that I would pass. Three days, 7-8 hours a day. I enjoyed it and I came out a slightly different person.
It’s affected the way I teach because I’ve come to realize how much I relied on remembering instead of understanding and discovering. There’s a faculty member, who’s a friend of mine, in the physics department we’ll call him Dan. I think he’s a poor teacher in some ways, great in others. He would say something along the lines of “Don’t remember, think!”
With that one phrase he may have been a more valuable instructor than almost any other. While I think he has trouble instructing he does do a good job of asking easy questions that require thought and resist remembering. It’s uncomfortable to be faced with your limitations and shortcomings, but its invaluable.
Over the years I’ve begun asking my students simple conceptual questions that require almost no computation. They might rely on units, simple pictures or other short conceptual connections. I then witness almost complete failure in the presence of computational competence. They can repeat, they can remember but they do not understand.
Who am I and what do I want to be? I could make excuses or sell them as reasons why I am where I am and how I arrived here. I’m much more of a mathematical physics aficionado than a mathematical physicist. Analogous to enjoying good wine but not making it. While I have no doubt that I’ll eventually solve some cute personal problems of interest and publish them, I have to say that I’m not disappointed that I haven’t. While I once wanted to obtain a tenure track position I no longer do.
I’m fairly intelligent and have enough passion to compensate but realistically I have no talent. Most researchers don’t. The talented folk blaze paths, come up with ideas so profound you wonder sometimes how you missed them. I’d rather work on understanding the great minds that are than carving out a small niche for myself. I do aspire to greater understanding and depth in mathematics but also in recreational math and in teaching and in outreach mathematics to children and to bringing in more art (of all sorts) into both my teaching, my learning and my outreach. A retiring mathematics faculty once chastised me for my wanderlust in mathematics and my inability to focus on any single area. He said I wouldn’t amount to anything and in a very real sense he’s correct, I will not amount to much in the halls of mathematics but there’s more to success and accomplishment than academic accolades though I have great respect for those (and this particular faculty member’s).
Like a child there is much that I delight in, revel in fact. I think that many of us seek faculty positions because we’re not sure where else to go. We need down time, lots of it. We generally can’t get enough of it. We’re not using that time to run errands or do chores, we’re furiously attacking the beautiful immensity of mathematics, science, philosophy and art. Faculty positions often let us share this enthusiasm with a captive audience which allows us to hear ourselves out loud without the stigma of talking to ourselves. It allows us access to like minded individuals, colloquia, and lots of days off. It generally pays reasonably well so we don’t have to live as paupers.
Adjuncts are paid much less than faculty but it’s not a bad job, neither is the position of instructor which is still much more junior to either assistant or associate professor. There’s a bounty of spare time and some opportunities to talk to yourself in front of others. You have access to intelligent and curious peers and a great library.
My goals are humble. Live small, leave the mainstream of American consumerism. Mind you, I don’t condemn it for it affords some of us to live in the eddies of its currents. The goal is to live simple, live free, and trade money for time. Earn less have more. What we thinkers all want are long luxurious expanses of time. Time to write, time to walk, time to sit and stare letting the knots of tangled thoughts relax and lower the impedance between our understanding and the thing we which to understand. Develop that understanding and then share it.
So while I consider myself a mathematician, I’m not a good one nor talented. I’m passionate, I love it, it is my an important part of who I am. This blog cannot be anything more, however, than the musings of an excited, poorly educated academic. This is why I write, to understand, to share, to learn and be honest with both myself and those who wish to read.