Here's a question that is often asked by American High School students with regards to math: "when will I ever use this?"
It seems like a simple enough practical consideration. Most professions don't require the calculation of complex differentiation. One can certainly be a happy and successful person without being able to solve a basic Algebra problem. How is Mathematics an essential realm of knowledge?
For the sake of disclosure, I'll add that I stopped studying math after my freshman semester at UCSB. The first professor in that college Calculus class was so dry that I couldn't maintain an interest, and since I didn't require additional math for my major, I didn't waste the time and money on it. That said, I've had brief conversations with math majors and the kind of stuff that they studied sounds interesting to no end.
I had been considering this notion over the holiday break. I feel I've outgrown the Cold War reasoning that more students should study math and science so that we can beat the Commies in the Space Race. My love for math comes from a much more compassionate place.
In doing my cursory research for this article, I found this column from The Washington Post: What is the Value of Algebra?, by Richard Cohen. In it Cohen supports those same adolescent suggestions that math is largely useless. I can't disagree more.
Here's the weird thing, I feel about math the way I feel about the arts, literature, philosophy, history, even religion and spirituality... it's all vital knowledge. I can attest that as a student I didn't enjoy the way that one subject or another was presented. I can certainly say that I didn't agree with some of the ideas suggested by my teachers; often later I found that it was my perspective that needed to change, while at other times, it was just that the teacher wasn't doing a good job of communicating the information. The thing that I have learned about learning on the whole is that simply because I don't understand something I should not assume that it's not worth the trying.
Putting this in the context of that first question, "when will I use this?" The concrete answer is that you might never use the specific proof that confirms the Pythagorean theorem. The larger answer as I feel it is that the skills you had to learn to make that proof (and possibly simply to understand and apply the theorem) are more worthwhile.
As I mentioned before I resent the notion that math is solely helpful to the military-industrial complex. No slight to my JPL and CalTech friends is intended. The workings of mathematics are fundamental and profound. Mathematics is like a philosophy or even a mantra.
Here is an outline of my understanding of and approach to basic Algebra:
1) Algebra is simple.
2) Write down a first notion (these are often called givens)
3) Write down that notion a second time with a minor alteration (in Algebra these are most often substitution or manipulation) - keeping in mind that one usually should work simply
4) Repeat step three until you find the requested result.
That's not very different from the way I would teach algebra to a middle-school student, save for the one-on-one practical examples that I won't demonstrate here. Practice (after good examples) is the thing that makes math easy.
In the writing of this I was reminded of Mr. Miyagi from The Karate Kid, who taught Daniel to Wax on and Wax off. In Daniel's rational mind he asked "why is he making me do all this housework?" If you've seen the film, you'll have an idea of what I'm suggesting. Make your body repeat an action and it will come easily. Make your mind repeat a specific meme and it will evolve.
There's a long list of ideas that can be learned from practicing math. The bits I want to appreciate most at the moment are related to the basic exploration of the world. There's that bit of Algebra where one starts with a basic expression. That's not different from starting from some point and ending somewhere else. The idea that one can take their first and continuing steps to understanding a concept that at first might seem alien is very powerful and appealing to me.
That one could study universal concepts that come without political dogma is even more beautiful to me. It's a way of sharing a viewpoint with the world.
Love isn't rational. Neither is math. I'll give this some more consideration before I continue.