# Riding the Integral

November 23, 2017

I walked into the old wooden structure one summer morning, and the smell of hay and sawdust filled my nose. Heat hadn’t corrupted the breeze just yet; there was a hint of the coming fall in the early morning wind that caressed my cheeks. I was the first human these creatures would see that morning. I offered my hand, graciously accepting the nudge of a velvet nose as a good morning from each horse. I left that structure, and a barn cat followed me as I walked one on? down? the stone path. I walked past the large riding hall, a classroom of sorts, a testing hall where my skills and capabilities would be put on show for all to see. A student of the art was already working hard to master harmony with her beast, performing an intricate dance that would never truly be mastered.

This practicing of practicing an art, in this case horseback riding, can be compared to completing math problems. Much like walking into the stalls, I enter a testing hall early in the morning and am greeted with the smell of freshly printed-paper. I pass rows of desks, and I touch each as I find my seat. Here my abilities as a student of mathematics will be literally put to the test even if I perform perfectly, there will always be more to learn. The beast I seek to harmonize with in this testing hall is not a horse, but an integral.

I never knew which horse I would ride when I came for my lesson each day. I stood nervous, and waited as my teacher scanned the list of names, sometimes giving silently commenting under her breath. “No, that won’t go well at all.” “Have you ridden that horse yet in a lesson?” Not knowing which horse I would get, perhaps the young spirited stallion or the calm dependable mare, is much like not knowing what math problem I will get on a test, a long intricate integration requiring critical thinking or a simple derivative I can do as well as I can brush my teeth.

The next step was forcing myself to come to terms with whatever horse I got. If it was one I knew, taking the creature out of its house, grooming the beast with soft brushes that unleashed the dust and dirty from hair, and tacking it up was an easy routine. If not, I tried to stick to the guidelines, the tactics I could always use, but keeping in mind I would have to adjust to that horse specifically. With some horses I have to nudge their shoulder so they pick up their hoof; others simply raise their hoof. The same goes for solving integration problems. Some I will have down to a routine, simply substituting in variables; with others I will have to adjust concepts so that I can come to an equation that will eventually grant me an answer.

Everything is in place, my heart beats faster, and the real challenge is ahead: actually riding the horse. As I put my feet in the stirrup I grip the reigns and swing myself on top of the horse. The first few steps are easy, getting used to the movements my hands make, and my fingers slowly adjust to the movements they will make to tell the horse when to turn, stop, change speed, or execute [parallel with tell] any other command. I remind myself that the worst that can happen is I embarrass myself by making multiple mistakes; everything from riding the complex task of riding the gait tölt to not being able to turn or stop a young horse because my foot isn’t in the right place and I’m doing too much with my fingers. Much like the mistakes I can make in riding are the mistakes I can make in math. On a test I may not able to complete a problem because not only do I not understand the concept, but also I continuously make small mistakes in the arithmetic.

Some may say a horse is not a math problem [One is alive and it eats and sleeps and can reproduce while the other is simply scribble on a page. The difference between the horse and the math problem is that a horse has a mind of its own. It may seem sometimes that the math problems deliberately create more challenges for you, seeking to entrap you in their wording or complexity. Some math problems are just beyond your knowledge. A horse may not intentionally work against you, but sometimes it does not understand what you want from it. The communication, after all, is even more up to interpretation than words. A slight increase in pressure by the lower calf can send a horse running, while slightly too much pressure on the reigns will annoy some horses, making them want to get away from you in whatever way possible.

As the lesson goes on, I don’t know if I’m making mistakes until it is too late. The horse starts tossing its head, angry at my actions. The teacher shouts across the hall, “Jana, you can’t tölt if half of the horse is in America and the other here in Germany, [comma splice] put your horse and your head together.” Some small things I myself can catch. If I notice the horse isn’t doing something right, I try to correct it. Shuffling things around, eliminating variables where I can. The math problem gets harder. My hands start to shake. My breathing gets faster. The math problem seems to be shaking its head at me, just as my horse would. Fear creeps into me, and my mind starts to go blank. Stop. Breathe. Count. 1, 2, 3, breathe. Reassess the problem. What are you asked to do? Whether you are working with the horse or the difficult math problem, the process is the same: complete a task with precision and beauty.

So to be truthful, riding a horse is no different than doing an integral. The same strategies are executed and the same internal panic ensues. Crying as a result of failure is common with both challenges, and both riding a horse and integrating require a lifetime of practice, and neither will ever be truly perfect.

Maybe that’s why before a math test, I imagine I am sitting on the small, white, Welsh pony Chameur, who taught me so much, but also threw me off more than any horse. He is the ability to overcome obstacles, both metaphorically and literally. As I continue my path as a math major, I try to remember there is very little difference between something that I call my passion, and a skill I hope to make money with, one day.

This piece draws on the similarities between what I do outside of school, horseback riding, and my major math. Both are my passion, but sometimes that's not always clear.