Television viewers in the UK have recently witnessed a major challenge to the hegemony of TV chat shows, TV chefs, ‘Judge Judy’ or programmes on house refurbishment. The challenge took the form of a series of programmes about mathematics that were devised and presented by the author of this book, the contents of which overlap with his televised expositions.
How successful was Marcus du Sautoy in his quest to persuade the UK population that engaging in mathematics is more meaningful than, say, watching the ‘Jerry Springer Show’? Perhaps we will never know; but many educated non-mathematicians of my acquaintance have told me that they were captivated by the range of ideas to which they were introduced via du Sautoy’s TV programmes. But isn’t the engendering of enthusiasm the main criterion by which to judge popular introductions to mathematics?
Marcus du Sautoy’s success is partly based upon his ability to show how a single idea may apply to widely differing situations. For example, in the first chapter of this book, prime numbers are used to explain why a certain species of cicada comes to life once every 17 years, and why Messiaen introduced 17-note rhythmic sequences into his ‘Quartet for the End of Time’. A myriad of other interesting situations are used to explain the prevalence and properties of prime numbers, and unsuspecting readers and TV viewers are gradually led into the arcane world of the Riemann hypothesis (Jerry Springer, eat your heart out!).
Although the title refers to ‘number mysteries’, the range of mathematical ideas in the book is much wider than that. The second chapter (The Story of the Elusive Shape) has readers blowing imaginary bubbles that encapsulate many results due to Plateau. The eponymous solids of Plato serve as a basis for explaining various designs of soccer balls, and such ideas ultimately take readers into the microscopic world of crystallography. A few pages later readers are introduced to basic visual topology, and, in no time at all, there is speculation on the shape of the universe.
The whole book is like this. Seductively interesting contexts are introduced together with relevant simple mathematics; but readers soon find themselves among deeper ramifications that are discussed from an historical and mathematical point of view. Probability is a central theme in chapter 3 (The Secret of the Winning Streak). Codes, from the boiled egg versions of 16th century Italy to the Enigma variation of WWII, are the main ingredients of chapter 4. A clue to the contents of the final chapter (The Quest to Predict the Future) is that it delves into Poincaré’s work on the three-body problem.
In short, Marcus du Sautoy is a first rate expositor who entertains, but never trivialises. Having captured the interest of the reader, he than engages him/her in mathematical experimentation, and his book will be enjoyed by anyone with an enquiring mind.
Peter Ruane’s journey into mathematics began during army service in 1957. It consisted of a thorough reading of Pendlebury’s 300-page Shilling Arithmetic.