Banana skins galore are scattered throughout a book for the hesitant maths reader, writes Ted Dewan

The jacket notes bark, “If you’ve always loved mathematics, you will find endless delights among the secret passages of The Magical Maze”. True. “If you’ve always hated mathematics, a trip through The Magical Maze will do much to change your mind.” Well... ummm...

Being an ex-physics teacher, numbers and I have always been chums. So I eagerly cracked opened Ian Stewart’s The Magical Maze: Seeing the World through Mathematical Eyes, his new book accompanying this year’s Royal Institution Christmas Lectures. There’s some neat stuff in here; some old favourites, some unfamiliar insights, and a tasty spread of mathematical goodies laid out for the lay reader. There are some wonderful insights into how mathematicians see opportunities for finding simplicity and structure everywhere.

Stewart’s sympathy for the hesitant reader is evident from the start. He begins by banishing “X” as his algebraic variable and instead chooses to use the early Egyptian term “heap”. “Heap” is represented by a grey drawing resembling a mound of mashed potatoes; refreshingly unnumberlike and just as good as dumb old “X” and its undeserved sense of mystery.

Most excellent is the introduction to the chapter on probability. It’s a superb analysis of the illusory “law of averages” many of us fall victim to when using our ill-equipped brains to grapple with probability.

But having enticed you into the maze within the first chapter (or “passage” as Stewart cleverly calls them - that is, passage in the maze), “X the Unknown” returns from exile and eats up the reassuring “heap” of mashed potatoes. Then you’re suddenly gored by the Minotaur; tedious-looking tables and equations bombard you. Of course a book about mathematics has to have numbers and equations in it, but their emergence is abrupt and at odds with the deal you think you’re getting at the maze’s entrance.

There’s a bothersome riddling Alice in Wonderland tone that creeps in, addressing those in-the-know, leaving the outsider confused. Geeky dungeons and dragons’ “junctions” appear at the beginning of each chapter, all referring back to the bewildering metaphor that appears in the book’s introduction. Although I appreciate this effort to intrigue and enchant readers, I found this whole metaphor distracting. Stewart is far more enchanting when he focuses on the mathematics. He clearly loves maths and his love is infectious much of the time. But perhaps this very maths-love made it difficult for him to apply a knife of mercy to the tangle of clever embroidery.

But even mathematical conventions are undermined by the inexorable whimsy. In one example, the Greek letter “pi”, traditionally used to represent the ratio of a circle’s circumference to its diameter, is used to represent “porridge”. It’s a good example of one of the many banana skins Stewart scatters throughout the book for amusement. OK, perhaps casting “pi” in the role of “porridge” serves to underscore the arbitrary nature of variables, but it’s hard to look at that little “pi” stonehenge and not think of “3.14”. Why not use that “heap” of mashed potatoes? It looked a whole lot more like “porridge”.

The rest of my criticism very likely has nothing to do with the author. I would first point the finger at an unimaginative editor, a miserly accounts department or the publisher to explain the quality of the book’s illustrations and diagrams. They are generally boring, confusing, and poorly laid out. Far superior and clear artwork appears on the instructions that came with the free travel alarm clock I got when I opened a new bank account.

I feel terrible knocking this basically nifty read because I share Stewart’s passion for communicating left-brain ideas to a lay audience. However, the late 20th-century “third-culture intellectuals” have transformed popular books about science and empirical thinking; the big bossy-like Dawkins, Gould and Sagan have elevated the state-of-the-art, making some perfectly fine books on the same shelves seem out of date and flabby by comparison.

Having said that, there are plenty of skilfully written goodies in The Magical Maze, such as how to use a toy train set as a computer and a study of the rhythmic patterns with which animals move their feet. With fewer tables, the dead ends blocked off, and a new editor and designer, the result could add up to something truly magical.

Ted Dewan taught physics before becoming an illustrator and a creator of non-fiction and picture books for readers of all ages. His most recent popular science illustrations appeared in The Axemaker’s Gift by James Burke and Dr Robert Ornstein, and his latest picture book is his “scientific” version of The Sorcerer’s Apprentice