I’m still trying to figure out what I think about that. I started in February of 1998, studying physics at Miami University (Ohio), and soon after decided that I might as well pursue a dual math/physics major. Some years later, logistical practicality prevailed, and I chose to study only mathematics. I’m still skeptical that I ever did.
I’d come to define myself, in part, in terms of this studenthood. Between first registration and final grade tally, I married once twice and divorced once. I saw two daughters come into the world, and one leave it. I bought a house, divested myself of that house, and bought another. I accepted the job I’ve had for a decade, and which I’ve spent the last few hoping to leave. Always, actively or in that part of my forebrain where ego and regret collide, I was a student.
And now I’m not. Now I’m “done.” I expect my diploma in the mail soon, and I will hang it in our office proudly. Though…though it’ll represent not so much a goal reached, but the closing of a personal epoch. An end to a struggle I never fully joined. A curtain call for the döppelganger, the ostensible student. And a beginning of my real education.
Not that I haven’t learned anything; that’d be a bit melodramatic and glib. I’ve learned that the Stewart calculus text is a credible device for (a) teaching various recipes for mathematical cooking, e.g., L’Hopital’s Rule; and for (b) scaring students into believing they’re “bad at math.”
I’ve learned enough of Riemann and Cauchy to have a first-order approximation of how much yet there is to know. I’ve learned some of the basic lexicon of mathematics, of continuity and metric spaces, of normal subgroups and homomorphisms. With a little review, I could even do something with them.
Which is to say, I’ve also learned what it is to truly study a subject. Well, actually, I suppose I can’t claim that: a recursively enumerable set isn’t necessarily a recursive set, which is to say that my knowing that I did not truly study a subject doesn’t confer to me knowledge of what it is to study it. Another first-order approximation, then. But useful nonetheless.
Now there is but to finally carry the mantel of student, freed from the illusion that completing repetitive problem sets on line integrals or expectation values actually constitutes more than a cheap rip-off of mathematics. What I’ve gleaned from this at-once trivial and enlightening realization applies not only to my development, but also to that of my children. What I’ve gleaned is that, even if these cobblestone streets were paved with good intentions, what we generally refer to as “education” is at its very best vocational training, and is at its very worst a commoditizing of our time and attention, of our will to power.
I failed as a student in more ways than I have the patience to note at the moment. Among this litany is my failure to form any academic community. I’m not sure how much I missed out on, but I bet it’s substantial. I’m a product of my passive-aggressive heuristic for dealing with people, characterized by idolizing my antisocial tendencies and then lamenting my lack of human connection. This failure as a student is my failure as a person, notwithstanding the logistical challenges a parent-student faces.
I’m officially done with this particular rant. I’ve really drained myself by alternating self-congratulation and “Woe is me.” I created what Carl Rogers might call a self-image at odds with reality: every Einstein quote, every time I watched Good Will Hunting, every browsing of Carl Friedrich Gauss’ or Terrance Tao‘s Wikipedia pages, contributed to the fantasy that I would, or more importantly, should, be similarly prodigious and capable. My particular knot of neurons and ganglia translated that information into a proscription against hard work, as if I shouldn’t need to work hard, as if instead I should need only to surround myself with the trappings of genius to free genius. And that, that’s the most important thing I’ve learned.
My most ambitious academic product is stored here (LaTeX file here). It’s an interesting, short paper I all but transcribed from my faculty advisor’s notes. I did learn a bit about computability, and LaTeX, and I enjoyed the process. Now I’m moving on, perhaps to study mathematics.