Assignment 6 — Theodore

    “Math problems only have one right answer, but in Art/English/Debate, each student finds a different correct answer.” I’ve heard multiple teachers say this (though not this year). They wrongly imply that math forbids imagination, only allowing the rote application of rules to numbers. That’s like asserting that a paragraph contains at least one sentence. True, but meaningless. In reality, mathematics involves curiosity and discovery (and fun). How do I know this? I’m experiencing it.

    In 2013, I needed a topic for my science fair project. Last year’s project had contained too much math for the behavioral science category, too little for the math category. To get help choosing a topic, I turned to two local mathematicians, my parents. Their suggestion eventually evolved into this: Find the relation  — if any  — between a modified version of the Pythagorean Theorem (the familiar a squared + b squared = c squared) and complex numbers. (If you want to know details, email me.) At the time, my vision of mathematics resembled yours; I wanted to discover one equation relating the two topics, just as a map links lines on paper to rivers and mountains. After all, short problems must have simple solutions. Long story short, that idea failed. I cobbled together five equations for the science fair, but they did not satisfy all potential cases. Disappointed, I forgot about the problem for six months.

    In the summer, without any homework to take up my time, unable to play outside in the stifling heat, I glanced over the problem again. I know what you’re thinking: “With more experience, Theodore found that he had overlooked a simple answer.” Nope. I advanced my comprehension of the question by an inch, then let it fall by the wayside as my family moved to another state. But I began to understand that my research might not end with a simple solution.

    Stop reading for a moment and think: Does this problem sound like any math problem you have seen in school? It defies an easy solution, defeats the techniques learned in Algebra, and takes months (soon to become years) to solve. Seems like a waste of time? Yet I kept coming back to it because it required original thought — not blind obedience of a textbook.

    Jump forward to now. Unlike my middle-school self, I know how to program a computer to check hundreds of cases. Surely modern technology easily handles math problems; my question is only a few steps away from the ancient Greeks. But Microsoft Word’s spell checker doesn’t write Shakespeare. Instead of a solution, my program opened another hole in my four-year-old hypothesis: To put it simply, no equation that I considered works.

Today, the problem remains almost as murky as four years ago.

So I failed again, right? Not anymore. Attempting to solve the problem forced me to develop programming skills, try independent research, and go beyond anything taught in school. To find an answer, I’ll need more imagination than for any project in art class.