When I was in high school, I nearly failed Algebra II. In the end, I pulled through with a C- and vowed to never take another math class.
What I know now is that my problem was not the teacher, but how I approached the subject. As young Mathematicians, we are taught to practice mechanical arithmetic over and over, and are forbidden to use our calculators on tests. The reason? Obviously because that machine can solve the problems easily. Taking it one step further, as a budding programmer I wrote programs on my home computer to perform the calculations that take so long by hand. By the time I entered my Algebra II class, I had it in my head that solving a problem always involved a logical progression of operations, and I was just waiting for my teacher to tell me the steps.
I don’t remember the exact problem, but I do remember the question I had: “where in this equation does it tell you to multiply through by 1/2 on both sides???” For the first time in my life, I just didn’t “get it.” I wanted my teacher to give me the step-by-step formula to solve for x. She wanted us to be Mathematicians.
This plagued me for the next couple of years. Most students would just abandon the subject and move on, but I had a bit of an ego about my intelligence. I SHOULD be able to understand it. Unfortunately I was still holding on to my mindset that everything in the world is deterministic and mechanical. I had come to the same conclusion that Newton had: if I were to have infinite knowledge about every particle in the universe at this moment, I could predict the future.
I was unable (or unwilling) to let go of my preconceptions and change the way I thought. It wasn’t until I retrained my brain that I came to truly appreciate Mathematics. Sure, it can be approached with rote computation and analysis, but the really beautiful discoveries come from the same place as paintings and music and dance. It is the process of creativity and it’s not easy to nail down how exactly it happens.
So now I’ve become obsessed with this. Although I’ve abandoned any ideas of formalizing creativity, I can’t help but wonder what a Mathematician was thinking when he or she came up with some particularly clever proof or method. I hope to use these pages to example this, in some cases to simply marvel, and in others to provide some insight to begin to explain “how did they think of that?”