Heading Off On a Tangent
Math is awesome. I am unwilling to hear any contrary arguments on this topic. Math is, unequivocally, awesome.
What’s not awesome is math education. This is not a novel observation. The problem of failing math education is well documented and well understood. To the extent that math education continues to fail (and as a recent computer science student I can tell you with confidence that it continues to fail), this failure seems more a function of bureaucratic inertia than of an absence of good ideas. Just because a problem is well understood doesn’t mean it’s easy to solve.
And that, right there, that last sentence is a perfect illustration of why math is awesome. Because the idea that a well understood problem can be hard to solve is something that makes sense to us in our language. It describes an experience of the world that intuitively appears to be true. If you study math long enough, you will discover well understood problems for which all of the tools we normally use to find solutions break down. It’s as if math is affirming our intuitive suspicion. We look at the universe and say, “man, there are some problems that are hard to solve no matter how well you understand them,” and the universe answers back, “I know, right?” Only in its own language, which is math.
The idea that math is “the language of nature” or “the language of the universe” is cliche enough that it probably doesn’t get enough critical consideration. It’s a metaphor that holds up beyond a superficial reading. In this model, the universe has information to share, but it can only communicate that information using math. It stubbornly refuses to speak any other language, so the only way to understand what it has to say is to try to learn math. The issue is that math can be hard to understand. People who devote a lot of time and effort into understanding it might only pick up the equivalent of a few words or phrases. One of the great innovations of mathematical thinkers has been to develop what are effectively trade languages between human communication and math — well formed systems of symbols and rules about which symbols are meaningful. Much of the failure in math education would seem to come from the assertion that these symbols somehow are math.
Everything I’ve written so far is a train of thought that is only possible for me to have because I have enough knowledge of math to be able to make these connections. The beauty of math is that it gives your thoughts a new medium in which to expand and explore and interconnect. If you think my thoughts are interesting or valuable, then you have no choice but to agree that math is awesome. QED.
The details of my experiences in math education are best saved for another day, but the highly abbreviated version is that I have had periods of greater and lesser confidence in my ability to “do math,” which is to say learn and repeat the specific symbolic manipulations associated with a particular type of problem. Lately I’ve been coming off a period of lower confidence, largely coinciding with a handful of bad educational experiences. Oddly enough, my experiences with periods of higher confidence have coincided with times in which I’ve had particularly good educational experiences. Huh. Isn’t that weird.
In the past I have thrown my hands up and allowed myself to be helplessly carried on the waves of shitty education. Had a bad instructor in calculus or linear algebra? Oh well, guess I’ll never learn those topics. Or at least I won’t until I find an instructor who gets me — an outlier whose teaching style corresponds with my learning style sufficiently closely as to be inspirational. Inspiration is great. It’s an amazing thing to experience and worth seeking out, but there’s no guarantee that it’s out there. Even if it is, there’s no guarantee that I’ll find it. Even if I do, there’s no guarantee that it will happen in a timely manner. Instead, if I’m going to gain a deeper understanding of math, I’m going to need to learn to take information that might be poorly communicated, consider it, break it down into its essential components and integrate it into my knowledge set in a way that makes sense. I can’t sit around and wait for someone else to break it down for me.
In my experience with learning, and especially with learning math, nothing is more valuable in solidifying information than teaching it to other people. Teaching forces you to think about things in new ways, to be prepared to answer questions, to synthesize connections between ideas that might otherwise have seemed wholly disparate. The problem with teaching is that it’s hard to do without a student, so…why not write about it instead? Writing can be addressed to an imaginary student and carried out as a largely solo activity. I’ve had some limited success with studying for exams by essentially rewriting a selection of course material in my own words, so I know that at least limited success is possible.
So that’s what I want to do with some of my writing energy for a little while. I want to write down everything I know about math. Or maybe more accurately everything I think I know about math. I’m sure I’ll have plenty of mistakes and omissions and just generally weird or bad ideas along the way. My primary hope is that in doing so I will find a more complete understanding of some of my favorite things to think about. My secondary hope is that someone reading it might find a passion for math that they didn’t know they had previously. Maybe it’ll be fun to read too. Who knows.
I think I’m going to do that writing somewhere that’s not Medium though. I want to keep my writings on here more loose and sketchy and not too weighted down by a single topic. Details TBD.