I have been teaching mathematics in an Australian High School since 1982, and I am a contributing author to mathematics text books.
It was one of those hot summer days, just before lunch. The air-conditioning was running a poor second to the humidity and windows were flung open in anticipation of the predicted cool change. Students languidly copied from the board whilst I explained how to solve quadratic equations. I might just as well have been describing how useful it is to make ice water in the arctic. Some feigned interest in what I was saying; most were waiting for the bell.
The door was slowly opened and all were thankful for the respite this event promised. The principal and a tall boy entered the room.
“Hello, everyone,” the principal began. “We have a new student. This is Manny. He will be in your class. I’m sure all of you will help him become a part of our school community.”
While the principal was addressing the class, the boy remained completely motionless, seemingly staring at some object through the window.
The principal finished his speech, smiled beatifically at Manny, gave me a “please take care of him” look and left the room.
Manny looked intimidating, almost menacing. Taller than average, of slim build and a dark complexion, his demeanour was accentuated by a concave nose, pointed chin and prominent ears. Long hair, earrings and Goth attire completed the image.
“Hi, Manny,” I began. “It’s nearly lunchtime. There’s an empty seat over there.” I pointed to a desk next to Jimmy. “I’ll talk to you next lesson about what we are doing at the moment.”
During lunch I was briefed. Manny was an orphan and was looked after by his grandmother. He had been in trouble and at his previous school was asked to ‘move on’. His reports were not enviable; ‘frequently truant, unco-operative, inattentive and prone to daydreaming’ were prominent behavioural descriptors.
Next day, Manny sat alone at the back of the classroom, near the window. He had somehow acquired our school diary, but he had no books.
I began my spiel. “Okay, today we will look at the relationship between the solutions to a quadratic equation and its determinant, where -”
“The discriminant,” a voice interrupted. It was Manny.
“I’m sorry, Manny. What do you mean?” I asked, slightly apprehensive.
“The discriminant,” he repeated softly.
Immediately I realised that he was right. Why can’t I ever remember the difference between discriminant and determinant?
By this time the class was totally absorbed. They saw the sword of Damocles. They wanted more. Could I redeem myself?
“Yes, of course,” I agreed and quickly added, “but if we have a pair of simultaneous equations then we could use the properties of the determinant.”
I tried to be convincing, hoping that the class –and Manny- would believe.
“No,” Manny continued. “The determinant is only valid for linear expressions.”
Game, Set and Match!
“Okay. I’ll check it up,” was all I could meekly offer as a reply. “How did he know?” was my summary of the situation later that day.
During the next class, while the others worked from their textbooks, I placed a sheet of paper in front of Manny. On it I had written a complicated mathematical expression whose solution was Euler’s number, denoted by e. Manny stared at it for a moment and continued to gaze through the window.
When the lesson was nearly over I decided to retrieve the sheet. It was exactly as I had left it. However, I noticed Manny had festooned the school logo on his diary with intricate geometrical designs and with insightful penmanship he had changed our school motto, Concordia Prorsum – ‘Forward In Harmony’ to ‘Forewarned Disharmony’. In the middle he had also written a large e. Euler would have been proud!
Next day, I wrote on the sheet a question asking for the square root of negative four, something only a university trained student would understand. Manny's reply was to scribble +2i, -2i (the correct answer) across several pages of his diary.
On the third occasion I challenged him with a convoluted problem involving integration of a trigonometric function whose solution is denoted by the greek letter, pi. Manny's response was to sketch a pie, complete with sinuous curves representing steam emanating from its pores.
This mathematical game of cat and mouse continued for another week. The class had their hero. I had a protégée.
And then, one day, his seat was empty.
“Where’s Manny?” I asked the principal.
“Manny’s gone,” he replied proudly. And then he explained.
“You noticed, of course, that Manny is a troubled but mathematically gifted student?”
“I figured as much,” I replied.
“Well,” the principal continued, “somehow he attracted luminaries from a leading university. They are prepared to adopt him, warts and all, and hopefully set him straight on a few things. And, of course, they hope Manny will do them a few favours mathematically.”
I kept track of Manny’s progress over the years, noting the impressive accomplishments and credentials he acquired along the way. And now I can be comforted by the thought that I may have had some part to play in the Professor’s mathematical awakening.