Book Review: The Joy of x
Steven Strogatz says that by arranging things in the right way, we can make a surprising link seem obvious — the hallmark of an elegant proof.
In particular, he’s talking about arranging a group of rocks — several groups of rocks, actually, each containing an odd number — to show that when you add all of the consecutive odd numbers, starting with 1, the sum is a square number:
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
I didn’t have to read The Joy of x to know that 1 + 3 + 5 + 7 + … + (2n + 1) = n2, and of course I’ve seen the visual proof that Strogatz demonstrated with a group of rocks:
But I don’t think that I had ever heard a definition for the concept of an elegant proof. Therein lies the beauty of Strogatz’s new book: while most of the concepts he covers will be familiar territory for the mathy folks who read this blog, each of the 30 chapters contains a pearl of wisdom, or an interesting factoid, or an eloquent sentence that makes you realize he’s as good with words as he is with numbers.
For instance, you probably didn’t know this about the distribution of heights on the online dating site OkCupid:
…the heights reported by both sexes follow bell curves, as expected. What’s surprising, however, is that both distributions are shifted about two inches to the right of where they should be. So either the people who join OkCupid are unusually tall, or they exaggerate their heights by a couple of inches when describing themselves online.
The chapters within the book are short and, as Strogatz admits, are not dependent on one another. You could start at Chapter 10, “Working Your Quads,” and it wouldn’t matter if you had read any of the nine chapters that precede it.
All in all, The Joy of x is breezy and fun, and while it won’t significantly further the education of a mathematician, it will provide some entertainment. And for the non-mathematician, it provides a nice overview of mathematics “from one to infinity,” covering everything from numbers to geometry to calculus, giving adults a second chance at the subject.