Seeing Through A Mathematician's Eyes

Sherman Stein is one of my favorite authors. He's written several books on mathematics, and even though he's a mathematician, he writes for the layman. In fact, one of his books is called How The Other Half Thinks, and in the preface he says the following:

One of my purposes in writing this book is to give readers who haven't had the opportunity to see and enjoy real mathematics the chance to appreciate the mathematical way of thinking. I want to reveal not only some of the fascinating discoveries, but, more important, the reasoning behind them...The thinking in each chapter uses at most only elementary arithmetic, and sometimes not even that. Thus all readers will have the chance to participate in a mathematical experience....

Other books I have of his are Mathematics: The Man-Made Universe and Strength In Numbers: Discovering the Joy and Power of Mathematics in Everyday Life. I'm teaching a low-level course this coming year, and I'm considering using some of his ideas and lessons in those classes to inspire interest in the subject.

I don't claim to be a mathematician. I have only a bachelor's degree, and that in applied mathematics; theoretical math has never interested me much. I want to use math. Yes, of course some areas that were once theoretical have shown themselves of practical value--prime numbers and the security of your ATM card, for example--but in general I like applying math to science and engineering issues.

Stein shows us, in his books, how math is everywhere, and how it explains so many things that we observe and marvel about in the world around us. His works came to mind when a former student sent me this article from the New York Times, called Math and the City:

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden. This week’s column is about one such pattern. It’s a beautiful law of collective organization that links urban studies to zoology. It reveals Manhattan and a mouse to be variations on a single structural theme.

Patterns. We math people sure love our patterns.

And even though it's in the New York Times, it's still an entertaining read--and one I recommend.