Numbers Are Your Best Friends presents a broad selection of mathematical problems, insights, theories, games, observations, even mathematical poems and mysteries, ranging from the simple and amusing to the demanding and abstract. But Van der Noort is even more interested in the feelings evoked by numbers, symmetries and patterns, since these explain what it is to be a mathematician. The result is a remarkable book of popular science, candid and perceptive, able both to enthuse readers and to move them.

Take prime numbers, whole numbers that can be divided only by themselves or 1. Are they part of an infinite series? Yes. Can we predict how many there are below a given number? No, say the mathematicians. Yet for all their intellectual efforts we cannot be certain even of that. We do know that they become increasingly rare, since the larger the number, the more smaller numbers there are that it could be divided into, but this tells us nothing about the distribution or even the prevalence of large prime numbers. Prime numbers, says Van der Noort, are fascinating but aloof creatures in the mathematical world, rather like cats, ‘and you can never be sure whether the affection is mutual’.

This warm, personal tone is what makes Numbers Are Your Best Friends far more than just another book about mathematical insights and trivia. Van der Noort genuinely loves numbers and is able to convince readers that such love is far more important, even to professional mathe- maticians, than technical skill or a highly developed brain. Numbers are personalities, and you are introduced to them in early childhood. You know how they think, how they feel and who they are. Some are good company, others are surly or supercilious. This is the foundation of mathematical insight, claims Van der Noort, and whoever studies mathe- matics (voluntarily or not) must learn to get along with them, for all their faults and virtues.

• It’s a shame that by the time they leave school, so many people have become traumatized by maths and seem never to get over their dislike. That fact was a major starting point for this book.
• A successful attempt to get people to be more aware of their irrational associations with numbers.