Cover of Alex's Adventures in NumberlandAlex's Adventures in Numberland by Alex Bellos (Bloomsbury, £18.99)

Unusually for a book about mathematics, Alex’s Adventures in Numberland is not written by a professional mathematician. Its author, Alex Bellos, is best-known for his acclaimed book Futebol: The Brazilian Way of Life, which looked at that country’s obsession with its national game, and he has spent much of his career working as a foreign correspondent. It is this experience of reporting from overseas that he draws on to write about mathematics – a dispatch from the land of numbers.

This approach to mathematics works incredibly well. Bellos puts all the skills he’s acquired reporting complicated news from far-flung lands to good use in elucidating mathematical concepts to those who may not be fluent in the lingo. Each section covers the historical background, and enough of the mathematical terminology, to equip anyone to follow the subsequent mathematical explanations. With elegance and wit Bellos manages to convey both the complexity and wonder of the world of numbers.

Beginning with the concept of what a number actually is (a far more complex matter than it sounds), Bellos embarks on a world tour of numbers from ancient Greece to modern Japan. As with all good travel books we get plenty of local detail and eccentric characters. In Japan he visits a Soroban (abacus) club full of rapt pupils learning complex mathematical formulas from a teacher “reading out numbers with the breathless syncopation of a horseracing commentator”. To explain the mathematics of the 3D shape known as the Menger Sponge, Bellos introduces a software developer in Massachusetts who has spent ten years of her life building a giant model from 100,000 business cards.

Mathematical classics such as the number 1089 (which is always the answer when you subtract any three digit number from its reverse and then add that answer to its own reverse, e.g. 421 – 124 = 297 and 297 + 792 = 1089) are inevitably included, alongside a wealth of other curiosities. Even when I thought I knew a topic back-to-front Bellos would throw in an example or idea that piqued my mathematical excitement and prompted me to reinvestigate. I had never before seen the Watts square-hole drill bit, which, because it takes the mathematically satisfying shape of a Reuleaux triangle, produces a square hole when it rotates.

One quibble is that Bellos occasionally strays into numerology. I know that some people find the challenge of looking for significant links between numbers and names, dates or events to be great fun, but I find it to be a blight on a subject that doesn’t require mystic sexing-up.

For those left with a phobia of maths from their schooldays, Alex’s Adventures in Numberland will not bring back bad memories. You might just find yourself with a newfound love of the subject, and you’ll certainly wish that Bellos had been your maths teacher. There is no one, including mathematics professors, who will not catch a bit of his infectious enthusiasm. You might even meet a new proof along the way.