To paraphrase Mr T, I pity the fool who doesn’t see the beauty of mathematics inherent in the world around us. As a teacher, I feel rather complicit at times in robbing children of the joy of mathematics. The systemic, industrial tone of education does not often lend itself well to the investigation and discovery that should be the cornerstone of maths; I find this particularly true in the UK, where standardized tests and levels are the order of the day. There are times when I am conflicted about how to cover subject matter. I have to find a balance between a breakneck schedule and a desire to achieve the comprehension that only comes with time and careful practice, strive to find the equilibrium between exploring interesting lines of inquiry and curtailing those lines in order to teach what’s on the test. I hope that as I become more experienced finding this balance becomes smoother. For now, though, it’s a struggle.
Because the secret that everyone learns as a child and then has beaten out of them by the endless grind of daily mathematics lessons is this: mathematics is not numbers. It is not arithmetic.
There, I said it.
I gave my students a test today on our statistics unit, which involved data collection: designing surveys, selecting sampling methods and sample sizes, etc. As they worked through the test, a few questioned its connection to mathematics. "This is words!" they protested, as if I were somehow an imposter trying to sneak extra English content into their day. Somewhere along the line—I don’t know precisely where—they developed this notion that mathematics is solely about manipulating numbers.
Really, though, mathematics is about relationships between things. Mathematics is a process for understanding the world, as well as understanding theoretical constructs that, while not directly observable in the real world, can still have useful and fascinating properties. Math can be numbers, but it’s also truth, in one of the most fundamental ways possible.
This is what Robert P. Crease attempts to communicate in A Brief Guide to the Great Equations. He foregrounds each equation and carefully explains how it became a part of the great canon of mathematics. He also explains why the result is so exciting, not just to mathematicians but to the population at large. I’m pretty enthusiastic about all this crazy math stuff, but Crease manages to stoke even my considerable flames of fanaticism and set my heart racing. The way he breathlessly extols the beauty and utility of Maxwell’s equations or Einstein’s relativity … it’s like a BBC Four documentary in paper form.
When it comes to books on popular mathematics, I always try to anticipate how a layperson would receive the book. As a mathematician, I don’t have a problem following the equations and explanations; it comes naturally. It still staggers me how some people are able to understand the intense nuances of some of the higher-level mathematics involved in quantum mechanics and relativity; I’m somewhat reassured by Crease’s claims that physicists often rejected new developments that required them to learn a lot of complicated new math. Yet I still know what Crease means when he carelessly bandies around certain terminology, expecting his reader to keep up to speed based on a high school education alone.
As far as pop math goes, A Brief Guide to the Great Equations is not the most friendly book. I’d probably hesitate to recommend it to casual readers, preferring maybe Zero: The Biography of a Dangerous Idea. For someone very interested in the history and philosophy of science, however, this book would appeal even if one’s math knowledge isn’t quite up to snuff. Crease recounts without fail some of the more interesting scuffles and disagreements among famous mathematicians and scientists; he also carefully lays out his own views on what constitutes a scientific revolution, and the role that developments of equations can have in revolutions.
It’s easy enough to follow the history and soak up the spectacle without following the math. I don’t mean to say that you shouldn’t read this unless you’ve studied math in university. If anything, Crease hopefully sheds light on how and why people can find math such an interesting occupation. By reading these stories of how Maxwell and Einstein and Schrödinger dedicated years of their lives to these problems, one gets the sense that the problems are more interesting and worthwhile than the equations themselves indicate. Crease explains how the problems consumed and intrigued these brilliant minds in such a way that, even if one doesn’t understand the nature of the problem—or its resolution—itself, one can still appreciate the passion and dedication involved.
Such passion and dedication are more universal than even the mathematics that unites the great thinkers featured in this book. One need not like math to be good at it or to succeed at it in school or in life. One need only appreciate its versatility, utility, and beauty. Crease tries and succeeds admirably in showcasing such attributes through the equations and history that he includes here.
Math is beautiful. You just need to open your mind, cast aside the "but I just don’t have the brain for it", and embrace the wonderful freedom of being able to figure out how the world works.