Review of Things to Make and Do in the Fourth Dimension by Matt Parker

I first heard about this on Quirks & Quarks from CBC Radio. Then Josie, one of my Canadian friends still teaching in England, was filling me in on how she went to one of Matt Parker’s stand-up events and how awesome it was. When I informed her I had purchased a signed copy of Things to Make and Do in the Fourth Dimension on the Internets, she was suitably envious. Not, however, as envious as I was for her singular stand-up experience—I don’t like stand-up, but I’d probably watch math stand-up.

Here’s my secret when reviewing math books: don’t focus on the math. Because, you know, anyone with a math degree can write about math. Writing about math is not hard. It’s making math accessible that’s hard. Now, that’s not because math is somehow more difficult for the average person to comprehend than any other highly-specialized field. We only have this perception as an unfortunate side-effect of our industrialized education system, which has traditionally insisted that we should learn math through rote memorization of rules.

Matt Parker rightly embraces a much more flexible idea about how we can learn math. Specifically, he champions recreational mathematics. That’s right, people: doing math for fun!

If you’re sceptical, I don’t blame you—see my point above about school systems. It’s really unfortunate we break people and squash their love of math so early like this. If I were better with young children I might consider becoming a primary school teacher to rectify this. As it is, my head stuck up here in the calculus clouds, I can only evangelize recreational math from afar.

See, we mathematicians know what people with a warped idea of math do not: mathematics is a creative discipline. Someone had to find the Fibonacci sequence, and they didn’t do it by looking at nature. Someone had to devise and name different dimensions of shapes. And mathematicians do this by investigating, by looking at what we already know and finding the gaps. Yes, they do this is a systematic way, and they have to do it rigorously before other mathematicians will agree with them. But a lot of mathematical discoveries have literally come about because of mathematicians just playing with numbers and shapes and ideas.

This idea pervades Things to Make and Do in the Fourth Dimension, which is organized in such a way to progress from basic ideas about numbers to very abstract ideas about functions, dimensions, and infinity. You’re not going to understand all of it, and that’s OK. Understanding everything is not the goal of reading a popular math or popular science book—getting a glimpse behind the curtain, understanding why it’s important, piquing your interest to learn more; these are the goals. (I’m trying to pump you up and help you be more resilient here, because I won’t lie to you and pretend it’s easy to follow everything, either in this book or in others like it.) Don’t worry though, because the author will always be around to help you out. Parker writes with a sense of humour that’s only to be expected considering his comedic career. (Britain really does seem to have cornered the market on funny mathematicians….)

There are also lots of practical exercises too. And I don’t mean questions you need to calculate and answer. I mean activities, templates for you to cut out and puzzles for you to consider. Parker is very proactive in demonstrating some of the practical ramifications of even the most esoteric ideas, from calculating digital roots to knitting 3D projections of 4D shapes. I could easily see some of this stuff working in a classroom setting if, you know, you’re not the kind of math teacher that thinks we should just memorize it all.

Really, when it gets down to it, this is how we need to be teaching and learning math. Reading a book about math is all well and good—I love doing it. But you need to learn by doing math. You need to try these things yourself, to investigate a problem until you hit upon interesting and sometimes unexpected results. This is one of the greatest things about mathematics: you can, in theory, verify every math result ever discovered by someone else. And you don’t even need specialized equipment: most of the time you just need a ruler, some scissors, and some paper. (And maybe a calculator or a computer for the recent discoveries!) This is DIY math at its finest.

I learned some neat things in the chapters that Parker devotes to higher-dimensional shapes. This is not an area of math I’ve studied in much detail, and conceptualizing higher-dimensional shapes is, of course, very difficult! Yet he explains it clearly. I also appreciate how much he uses computer programs to help him investigate relationships and ideas. As someone who also enjoys writing Python scripts, I’m always happy to see my interest in math and computers come together.

On the flip side, I know a lot about graph theory and enjoyed his section on that. He doesn’t really do anything new when it comes to talking about old chestnuts like the Four Colour Theorem and its infamous proof. Nevertheless, this is one of those areas of math that people never hear about unless they go into university, despite it being so interesting and widely applicable.

Things to Make and Do in the Fourth Dimension is a lovely and informative book. It’s a great example of how to write well about doing math for fun. Parker is ever-encouraging, ever-understanding, ready to make fun of math, mathematicians, school, and himself—and yes, my dear reader, you as well. This is a safe book in that sense: you’re not going to be judged for not liking math or not having much luck, so far, with it. But thanks to Matt Parker, you can roll your own math and enjoy doing it. We need more books like this! Until then, read this one.