The Enduring Value of Rigor

Spring Break at my institution has begun, and so I had a little extra time today to do something I’ve been wanting to do for a while: visit my alma mater. I took the two-hour drive south with my son, who planned to work on homework there while I got ahead on my work goals for break. It turns out that we’ve visited right in the heart of my old stomping ground’s midterms. I’m having flashbacks, man. I think I have chills.

We had a very difficult time finding an empty desk. All four floors of the Engineering Library are packed to capacity with students studying. Some of them are studying alone. Others are sitting at tables where tutors and TAs are hosting study sessions. Many are staring at computers, typing frenetically or sketching out solutions on a tablet. The nervous energy here is palpable. There are a lot of frowns and furrowed brows, and a collective countenance of exasperated befuddlement.

Entire rooms have been set aside for tutoring the sequence of Calculus courses engineering students take. I chuckled to myself. “Pfffmph … Calculus. When was the last time I used that?”, as if I had forgotten that I’m Chair of the Math Department at my institution.

The irony of my involuntary betrayal of my current academic position could be forgiven, I think. Nostalgia had overtaken me. I was back in my late-teens-through-late-twenties holy land, thinking I was training to become an electrical engineer, quickly reliving my first few jobs in that field. Truthfully, counting on one hand the number of times I actually had to do math on the job during those days involves more math than those jobs did. The only time I ever used advanced mathematics after learning it as an undergraduate student was for my master’s thesis and Ph.D. dissertation and occasionally for an academic paper. Other than that, I never directly used all the math I took. I never found myself on the job working out the kinds of problems these sleep-deprived, stressed-out students were trying now to cram into their heads. So, I think my inadvertent chuckling was really nothing more than an instinctive lament of “You poor suckers!”

And yet, I know with absolute certainty that I wouldn’t have accomplished much of what I’ve managed to do as a professional, whether as an engineer or a software developer or a cybersecurity professional or as an instructor or as an educational administrator, if I hadn’t taken those Calculus courses and more. Calculus I, Calculus II, Calculus III, Differential Equations, Linear Algebra, Real Analysis – that’s a punisher’s row of academic litmus tests designed to put your brain through the intellectual equivalent of HIIT Cardio. And that counts just the math coursework. How about all those Physics courses, or the Computer Science courses I took that still, to this day, scare me every time I hear someone refer to homework assignments as “machine programs”. Or the Optimal Control and Adaptive Control courses I took in graduate school, for which I had to get past my mathematical Achilles heal – probability and statistics – to minimize control functions shaped by stochastic processes. Did I actually do all that?

I thought back on taking that daunting mix of courses simultaneously, in a fifteen-week semester, occasionally pulling all-nighters even though I almost never procrastinated and studied daily and started my homework as soon as it was assigned, just so I could master all the material I thought I’d be using every day of my career. I thought it was important to become an expert in the material, because surely it would come in handy as I solved real engineering problems. Right?

In my experience, none of the material came in handy for any specific problem. And yet, it has come in handy generally for every single problem I’ve faced. It seems to me that, unlike our musculature and cardiovascular systems, which atrophy and become less efficient when we stop physical training regimens, the effects of “cranial cardio” and “brain lifting” persist long after the intense workouts cease – even decades later. Exposed to enough rigor and rising to its challenge, you expand your brain in ways that keep it stretched. And that serves you well in every problem-solving exercise, even for problems that don’t involve calculating triple integrals.

Shouldn’t the fact that I’ve hardly applied what used to burden me so thoroughly during my academic boot camp years upset me? Shouldn’t I feel cheated? I don’t at all. On the contrary, I feel thoroughly indebted to the experience.

I now find myself looking at the students around me, frantically studying for their upcoming midterms, with a knowing smile. “Someday, you’ll be thankful for this!”

About Ray Klump

Professor and chair of Mathematics and Computer Science Director, Master of Science in Information Security Lewis University,, You can find him on Google+.

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