The Beauty of Numbers in Nature: Mathematical Patterns and Principles from the Natural World by Ian Stewart (review)

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Ian Stewart has written many books, so he has nothing to prove in terms of being a successful author who explains difficult topics in an accessible way. This book seems to be very close to another of his, first published in 2001, called What Shape Has a Snowflake? (Ivy Press). The present version, also with this publisher but with MIT Press as well, has improved new pictures as well as a better title, though the text is more or less unchanged. The text does not need to change, although some on page 162 shows its age. Ian Stewart is the David Attenborough of the genre and his style is fluent, readable, informative and confident.

This is a splendid book. The excellent prose is enhanced by spectacular pictures. It is breathtaking in its scope, and the layout is refreshing. Each topic is confined largely to just two sides—the open page. The book is so well written, with no wasted words, that this works. There are three parts: Principles and Patterns, The Mathematical World, and Simplicity and Complexity—16 chapters in all. The first three start with snowflake hexagonal symmetry, honeycombs, then other two-dimensional curves from nature, finally introducing three-dimensional patterns. This leads to the middle part of the book, the largest, with over 100 pages (eight chapters) that go into more technical detail. Stewart somehow does this without the need to understand any actual mathematical symbolism. It is a tribute to his explanatory powers that he succeeds. Here the section on animal stripes stands out, as does that on animal gait; these are research topics for Stewart, but once more there’s no mathematics here, just clear exposition. There is much more, from astronomy to architecture, patterns in time, even packing fruit in a box. The final section, five chapters, goes into complexity, fractals and chaos. The book is philosophical, beautifully written, artistic and with a touch of humor (Stewart has coauthored with the late Terry Pratchett and written science fantasy). Stewart has authored many books, all worth reading. This just might be the best of them.