book review
Bill Bryson  he's a travel writer isn't he? He goes places and writes about them, tells amusing anecdotes about things he sees and people he meets, making his readers laugh at the same time as teaching them something about the places he visits?

Early in our mathematical careers, we are introduced to prime numbers. These special integers, which possess no divisors other than themselves and 1, are the building blocks for all the integers. Thus an understanding of the properties of primes, including where to find them, is an essential part of number theory, and any serious discussion of prime numbers will inevitably lead to what is arguably mathematics' greatest unsolved problem: The Riemann Hypothesis.

Geometric dissection is the mathematical art of cutting figures into pieces that can be rearranged to form other figures, preferably using as few pieces as possible. You may already have come across puzzles such as the Aviary Tangram, the pieces of which can be used to form an egg, a chicken and many other shapes; but the ingenuity of the dissections shown here may still be a revelation to you, as they were to this reviewer.

The Four Colour Theorem  the statement that four colours suffice to fill in any map so that neighbouring countries are always coloured differently  has had a long and controversial history. It was first conjectured 150 years ago, and finally (and infamously) proved in 1976 with much of the work done by a computer. The published proof relied on checking 1432 special cases, which took more than 1,000 hours of computer time.

George Szpiro has a most unusual day job for someone writing about the abstract world of pure mathematics. Although he first studied maths at university, he has been a political journalist now for a number of years, working as Israel correspondent for NZZ, a Swiss daily. He wrote this book at night, after the paper's deadline, and as it was being finished lost one of his closest friends in a suicide bombing. The contrast between sphere packings in three dimensions and his daytime subject material must often have struck him.

Many people, when they look back, can pinpoint the precise moment when their interest in mathematics was awakened  it was when they found a puzzle that intrigued them. Perhaps they now realise the puzzle was trivial or insignificant, but at the time something about it captured their imagination and started them on a path that may have led very far  perhaps even into fundamental mathematical research.

Ballet and mathematics  not a combination that you often come across, but one that works beautifully in Frederick Ashton's 1948 ballet, Scénes de ballet. From the geometric patterns on the men's tunics and the perpendicular angle of the ballerina's tutu, to the movements and positioning of the dancers themselves, this ballet is a celebration of mathematics. Ashton was inspired by mathematics, and, according to the programme notes, used a system of Euclidean geometry to choreograph the piece.

Not many books about maths have chapters that start "The dead man seemed to stare at me in a most disconcerting way." But maybe more should  this book is a highly entertaining read, crossing sound mathematical exposition with the classic Sherlock Holmes style of investigation.

Many popular books about mathematics combine elements of exposition and personal commentary, but few combine these disparate elements to the same extent as this book.

This video, aimed at students aged 16+, opens with Professor Chris Budd holding the plastic yellow duck he is entering in the Annual Bath Plastic Duck Race. Competition is stiff  there are over 3,000 contestants  but how can we predict who will win? Very few competitors have form, and it's hard to tell much about their training regimens... so is the outcome totally unpredictable?
