The Most Useful Algebra Lesson Of All

I first encountered algebra in the sixth grade. Numbers disappeared–or at least, were consigned to secondary importance–and letters, mysterious ones like x, y, z, took center stage.  A mathematical expression called the ‘equation’–an incomprehensible sentence underwritten by an esoteric grammar–emerged on my intellectual horizon. (Strictly speaking, my teachers were rigorous enough to call these things ‘linear equations’ but all I could remember was the second word.) The rules for manipulating it, and triumphantly emerging from these machinations with the value of x held high as a trophy for all to see were, as my descriptions above might indicate, utterly incomprehensible to me. I stepped into the water and I immediately floundered, casting about in panic.

Unwilling to seek help outside the confines of my classroom–I did not press my brother, two grades senior to me, or my parents, for assistance with my lessons or my homework, which I was often submitting incomplete and incorrect–I was setting myself up for disaster. The axe fell eventually. In the first of the year’s so-called ‘terminal’ exams–because they were staged at the end of an academic term–I obtained a grand total of sixteen ‘marks’ out of hundred. It was an ‘epic fail,’ long before that term had acquired any currency.

Unfortunately, my fame in this domain of academic achievement did not, and indeed, could not, go unnoticed. My grades were noted on a ‘progress report’ and I was asked to bring it back to school, duly signed by my parents.  When I, hoping to escape the wrath of my father, showed it to my mother, she took one look at my math grade and told me he would sign the report instead. (This transference of responsibilities reflected a traditional division of parental labor when it came to my education; my mother helped me with the ‘humanities,’ my father with the ‘sciences.’)

My ‘interview’ with my father did not go well. He was perplexed by my grade, but even more so by my exam answer-book. I had executed some bizarre, inexplicable mathematical maneuvers, strewing symbols and numbers gaily all over its pages, thus allowing my teacher to grant me a few charity points for visible effort. Most embarrassingly, my father was able to surmise I had cheated, for I could not explain why certain moves had been made by me. (Indeed, I had; I had sent several panicked sideways glances at my neighbor’s answer-book during that fateful exam.) My mother sat close by, watching this interrogation–and my discomfiture–quietly. I could see my father’s visage tautening, his nostrils flaring. A stinging slap that would inflame my cheeks and set my ears ringing was probably headed my way. This was a man who had brooked no incompetence in his subordinates in his days in the air force; he would not stand for this display of stupidity and confusion on my part.

My father finally spoke, “Go get your maths book.” I complied. My father pulled out a notepad and a pen, looked at me, and spoke again, “Algebra is easy if you follow the rules.” I had no idea what those were.

I soon found out. My father explained to me what variables, constants, and coefficients–fractional and whole–were;  he told me I had to “bring all the variables to one side, and all the constants to the other”; I was supposed to “change signs when you change sides”; and so on.  It was not smooth sailing: on one occasion, after I had failed, yet again, to internalize one of my father’s instructions and committed a howler, he, overcome by exasperation, turned to my mother and confessed he would like to throttle me. I quaked and quivered, but he did not make good on that threat. He did though, tell me he would not let me go to sleep till I had mastered the art of solving linear equations.

The night wore on. My mother went to bed. My father and I continued to work through one problem after another. Slowly, algebra became comprehensible; indeed, it made perfect sense, and even began to appear as a little bit of a lark, a sleight of hand, a riddle with a key that could be made to work for you, and not just wizards and magicians. It was entirely plebeian; the masses could partake of its pleasures too.

Finally, my father assigned a set of problems for me to solve and bade me go into the living room to work on them by myself. If I solved them correctly, I could go to bed at last. I got to work; my father began his bedtime ritual of changing clothes and brushing his teeth. A few minutes later, he opened the door of the living room to check on my progress: Was I moving along? I said I was.

Once I thought I was done, I took my work over to my father. For a minute or two, he sat there, looking impassively at my scribbles. Then, he looked up and said, “Good work; go to sleep. You’ve got it.” I complied again.

I never became a mathematician. But I never feared the ‘lazy man’s arithmetic’¹ again.

Notes:

1. Legend has it that this is how Einstein’s father explained the heart of algebra to him: ‘you just act as if you know what x is.’