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I remember being good at math as a child. I remember enjoying the process of figuring out the problem. I really loved it. At some point that love switched to cold application: an algebraic sum here, a stat there. Mathematics became nothing more than a way to get to the answer, there was no beauty, and certainly no love. You figure it out, get the answer, and move on. That was my use of math for twenty years. Then, in my late thirties, I decided to go back to school and complete a bachelor of science. This meant I had to do a full year of calculus after a two decade long hiatus from anything that I recognized as a derivative or an integral. My brain bled. I kid you not. I spent hours doing problem after problem after problem. And throughout this year, two lessons started to unfold.
My first lesson is echoed by Einstein’s quote: It’s not that I’m so smart; it’s just that I stay with problems longer. In a world that seems so intent on speed, math forced me to slow down. In calculus we learn to see the importance in the smallest of line segments, to appreciate the beauty of approaching infinity. The key word is approaching. I had to accept that I was never going to reach x. I did not need to reach x. In fact, our ability to create most engineering feats and computational algorithms depends on us simply modeling infinity – the path to x. All of a sudden, understanding the path of a destination and what lies within it is the point. So, slow down and appreciate the journey. In calculus that journey provides the basis of appreciating its true power. I wanted to do well in my calculus class, and in order to achieve that I needed to come to realize the slow beauty of how this field of mathematics approaches its problems. Life is like this too. Getting my house cleaned quickly so I can get to the next thing doesn’t seem as important as appreciating my home while I tidy. Rushing my kids to school is not as important as enjoying my time accompanying my dear little ones as they begin their day. I simply need to stay within my ‘problems’ longer, and somehow life’s true powers manifest.
My second lesson is represented by an oft used internet quote: Math may not teach us to add love or subtract hate but it gives us hope that every problem has a solution. In psychology we learn about a construct called learned helplessness. This is the situation that can result when humans endure an aversive environment or condition and give up trying to escape it, because they see no solution, no way out. We no longer feel any control and therefore do not attempt to make it better. This is not a healthy psychological state, for an individual or a society. Calculus could have gone that way for me: this is painful, I have no way out, and so I will put up with it and not do anything to change it. Thankfully, I am not prone to learned helplessness. Instead, I worked really hard. Really, really hard. Slowly, each problem became less painful and more intriguing; each equation less intimidating and more revealing; each class less agonizing and more insightful. I started to look forward to my calculus work. By the end of my two semesters, I was able to solve problems I would never have been able to tackle when I started. Problems I would have had to pass off as not having a solution, at least for me. Life is like a class of calculus, you may not know going in, but with hard work and determination, you can figure it out. I can figure out how to add love and subtract hate. Math taught me to appreciate that.
Now, I was also very lucky to have two patient, intelligent professors who even managed to bring aspects of humor to a complicated subject. I remember one saying, “I know this is crazy, isn’t it?! But don’t worry, we will get there in the end.” And we did, although it took six full chalkboards and an hour of time, he got us there. Without my teachers’ guidance and open doors I am not sure if the two lessons described above would have come to fruition. To this end, I offer my sincere gratitude and humility.
Now I am on the doorsteps of my degree. I have learned many lessons going back to university, and although I am sure the formal education in my discipline will serve me well, it is the deeper lessons such as those found in my calculus classes that will most enrich my life and shape how I see the world around me. Math is more than getting from A to B, it is about the infinitesimal moments and paths that actually mean everything. My world is full of moments and paths. Math has taught me to not only see them, but to fully appreciate what they afford me: love and beauty. What more can any of us ask for?