Review of How to Solve the Da Vinci Code And 34 Other Really Interesting Uses of Mathematics by Richard Elwes

Really, it’s my fault that mathematics gets such a bad rap.

And by me, I mean math teachers in general. And by math teachers, I actually mean the pedagogical paradigm in which most of us are embedded, and the questionable premises of the educational system that encourages such pedagogy. Math anxiety is often caused by general test anxiety, combined with a lingering sensation that there is “one right answer,” as well as a misunderstanding what math is and how we use it. Other factors: parents communicating anxiety/resisting innovative ways of teaching, and a generalized anti-intellectual snobbery in our society in which those who are interested in how the world works are “geeks” and “nerds.” (This is independent of the fact that, in recent years, geekdom and nerdery has become trendy. Capitalist structures might be co-opting the symbols and fashions of geek culture, but that doesn’t translate into broader tolerance or embracing of geek interests.)

With How to Solve the Da Vinci Code and 34 Other Really Interesting Uses of Mathematics (I hate the title), Richard Elwes sets out to make some of the most important fields or problems in math more accessible to the layperson. This is a worthy goal. From the titles of his other books, it looks like this is Elwes’ pet cause: he likes to break mathematics into small but fascinating facts, problems, or ideas that he can explore in five-minute chunks. As a result, this is the sort of book you can dip in and out of, say at bedtime, for a number of evenings. You don’t have to remember a lot or pay attention to a plot.

Nor does Elwes demand much in the way of memory or understanding. He covers some of the basics of algebra in the earlier chapters, but even understanding those is not a requirement. This book doesn’t so much teach you mathematics as it describes the different types and fields of mathematics and some of the most interesting results or problems from them. Perhaps the most complicated concept you really want to understand is prime numbers: if you know what those are, then you’re good.

Some of Elwes’ explanations are great. Within this are many “standard” explanations that I’ve seen before and skimmed—that being said, I am a mathematician and a math educator and a math enthusiast, so what’s familiar to me is not necessarily familiar to you, and this might be someone’s first exposure to Russell’s paradox or the theory of sets or graph theory. So that’s not a negative in my book, just an observation that the more mathematically-inclined have likely come across most of the content here, in one place or another.

On a related note, I want to stress that this really is a survey of mathematical results. Some chapters are longer than others, but none go into the type of depth one wants for a truly comprehensible explanation of what’s going on. To reiterate: you won’t learn a lot of math here; you’ll learn about math. Also valuable and important, but it’s a keen distinction.

For me, some of the highlights were: Chapter 7, “How to unleash chaos” (chaotic systems and strange attractors); Chapter 15, “How to arrange the perfect dinner party” (Ramsey’s theorem); Chapter 18, “How to draw an impossible triangle” (non-Euclidean geometry); Chapter 19, “How to unknot your DNA” (knot theory); and Chapter 23, “How to build the perfect beehive” (2D/3D tesselation and packing). I like these chapters because they taught me something or reminded me of something I had forgotten, or Elwes’ explanations are particularly thoughtful and useful. For example, the knot theory chapter doesn’t just talk about knots—as the title implies, he mentions DNA, enzymes, proteins, etc. It’s a reminder that mathematical discoveries end up having applications in places you wouldn’t suspect.

That’s another thing that this book does well. In chapters such as the one on the four-colour theorem, or Benford’s law, Elwes emphasizes two important and related things about mathematics. Firstly, mathematical discoveries don’t always happen in isolation or as strokes of genius. We tend to tell those stories, because they are exciting. But for something like Benford’s law or the four-colour theorem, the discoveries build on decades (or centuries) of work. Several mathematicians independently notice something cool, make a conjecture, fail to prove it, and discard it—only for another generation to succeed where they didn’t. Math is a progressive, ongoing effort.

And something we don’t make clear often enough in the classroom is that new mathematical research is still ongoing at a furious pace. We present math as an accomplished, finished product: here’s how you find the missing side of a triangle; the Babylonians knew how to do it, and now you do too! But like science, mathematics isn’t a stable set of knowledge. It behoves us to raise awareness among the general public of how people research math and what we still research. Elwes points to the Clay Institute’s Millennium Prizes as one example. He also mentions a few other questions that remain open problems. While it’s true that genuine mathematics research is not for the faint of heart or the interested amateur, that tends to be true of any specialized discipline. Math is not necessarily more difficult or special in this regard.

How to Solve the Da Vinci Code is not the warmest of math books I’ve read. Elwes’ tone is conversational, yes, and has a hint of humour to it. However, the broad strokes of his descriptions necessarily make them less personal than they might otherwise be. He tells a story in most of the chapters, but it’s not with the same level of vivacity that other authors often employ. Instead, his style is one step up from an encyclopedia article. Again, this isn’t really a positive or negative in and of itself—it depends on what you want from a book like this. I, personally, want to know more about the author. I want to know where they’re coming from, what interests them, and hear them tell the story of mathematics from their perspective. We don’t get that here—Elwes never inserts himself into the text—and I feel like that’s unfortunate. But others might find it more objective and informative.

Would I recommend? Not for someone like me, who has read a lot of math books and studied math. For neophytes and laypeople? Maybe, depending on the person. I’d rather find a book that gets them more excited about one specific thing, rather than throw everything at them like Elwes does here. Maybe this book is best for someone who already likes math, has a passing interest or understanding of it, and wants to sort of survey the field and see what kinds of things are out there. In that case, there’s definitely 35 good ideas here.