Keith Devlin Makes Math Interesting
Keith Devlin is a professor at Stanford who’s teaching a MOOC (massive open online course) called “Introduction to Mathematical Thinking.” Here’s an excerpt from his first lecture:
“I’m going to start off with a question. What is Mathematics? That might seem strange given you’ve probably spent several years being taught math. But for all the time schools devote to the teaching of mathematics, very little, if any, is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. Well, that’s a bit like explaining soccer by saying, it’s a series of maneuvers you execute to get the ball into the goal. Both accurately describe various key features, but they miss the whats and the why of the big picture. If all you want to do is learn new mathematical techniques to apply in different circumstances, then you can probably get by without knowing what math is really about. But if that’s the case, then this isn’t the course for you.
One thing you should realize is that a lot of school mathematics dates back to medieval times. With pretty well all the rest coming from the seventeenth century at the very
latest, virtually nothing from the last 300 years has found its way into the classroom. Yet, the world we live in has changed dramatically in the last ten years, let alone the last 300. Most of the changes in Mathematics over the centuries were just expansion. But in the nineteenth century, there was a major change in the nature of mathematics. First, it became much more abstract. Second, the primary focus shifted from calculation and following procedures to one of analyzing relationships. The change in emphasis
wasn’t arbitrary. It came about through the increasing complexity of what became the world we are familiar with. Procedures and computations did not go away. They’re
still important. But in today’s world, they’re not enough. You need understanding.”
And what you need to understand, Devlin goes on to say, is that mathematics today is “the science of patterns. According to that description, the mathematician identifies and analyzes abstract patterns. They can be numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on. They can be either real or imagined patterns. Visual or mental, static or dynamic, qualitative or quantitative, utilitarian or recreational. They can arise from the world around us, from the pursuit of science, or from the inner workings of the human mind.” Read more about the course here.
I wish one of my math teachers had explained mathematics to me in this way. I could never see the point of math, but Devlin makes it sound urgently important for understanding the world around us. Did you have a teacher who helped you see math in this broadly important way?
In 10th grade, I took geometry class (as many 10th-graders do). I don’t know how it’s taught now, but when I took it (in 1976), we studied Euclidean geometry and we were taught how to create proofs of propositions. I still remember exactly where I was sitting when I finally did my first proof and understood what they were about. So, that was my first taste of real math.
Unfortunately, after that geometry class, I didn’t get the chance to do proofs again until after college calculus, when I took abstract algebra. And that’s when I declared my major as math.
It’s a shame that most people only know of math as computation. I’ve read some of Devlin’s books and he’s the right person to expose people to what math is really about. I’m hoping he’ll teach some more advanced math MOOCs in the future. I’d love to take an advanced class from him.