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I was always a high achiever academically in school, and my favorite subject was math. I got into a “fast math” program that taught Algebra I and II in middle school. I loved it, and I now wish I remembered the long-hand way to compute square roots I learned in that class. The next year, as a freshman in high school, I took geometry (typical for a 9th grader) and pre-calculus (decidedly not typical). The end result was that by the time I was a sophomore in high school, I had run out of math classes to take at my high school (pre-calc was as far as my small school went). The solution we came up with was for me to take evening math classes as a local college.
Now, I need to set the stage here a little bit. First off, I was small for my age and looked very young. As a 10th grader, I looked more like an 11-year-old than the 15-year-old I was. I was also not yet old enough to drive, so my mom had to drop me off and pick me up for the classes.
I was also very engaged in my classes (well, except maybe history and English). I had not yet learned that adults tend to only participate if they have to, and don’t offer any answers that they think might be wrong. I didn’t mind speaking up in class and asking the teacher questions about our work.
Finally, this being an evening class at a small, local college, everyone else in the class was taking it because it was a requirement to get their degree. Generally, these were engineers (from DuPont) working towards their masters degree in their chosen field. Assuredly, none of them had the passion for the subject I did.
So one evening, as the class was wrapping up, the teacher was going over our homework assignments for the next class. One of the problems had to do with the slopes of tangent lines on a parabolic curve. The teacher happened to mention that parabolic mirrors are very useful in the real word, because incoming light rays would all be reflected back to a single point (the focus). I thought this was really cool, and I asked about that in class. I don’t recall exactly what I said, or the subsequent discussion the teacher and I had (while the rest of the class remained silent), but the end result was that the teacher added to our homework: we were to prove that parabolic curves actually do focus parallel light rays to one point.
This sounded like a fun challenge to me. I couldn’t wait to get started on it. But even I realized that adding to the homework assignment would not be universally celebrated. Indeed, I was the only student who thought this was a good idea. The class was dismissed and I went to my mom's car, as she was waiting for me in the parking lot.
Since then, as I think about that event as an adult, I imagine what those other classmates must have told their spouses and families when they returned from class that evening. Surely having a little kid in their Calculus class, showing frequent exuberance for the subject, was a curiosity or maybe even an amusing addition to the class. But the evening I added an analytical assignment to their homework, I doubt I was quite as entertaining. My wife is taking evening classes towards her doctorate now, and so I am acutely aware of how precious her time is.
I don’t recall receiving any direct animosity from my classmates that evening, which I’m sure was a testament to their good nature. So to all my classmates I burdened with an additional assignment, I apologize. I hope the personal time I cost you was balanced by the pleasurable satisfaction you felt upon solving an interesting math problem. But probably not.