## Articles

**Artur Ekert**takes a tour through the history of codes and the prospects for truly unbreakable quantum cryptography.

**Claire Ellis**tells us about their heroic efforts, which historians believe shortened the war by two years.

**Andrew Stickland**explores the dangers that face the unwary when using a single number to summarise complex data.

**Lewis Dartnell**explains, our brains have evolved to take pleasure in rhythm, structure and pattern. Since these topics are fundamentally mathematical, it should be no surprise that mathematical methods can illuminate our aesthetic sense.

**John Baez**declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.

**Lewis Dartnell**looks at the vector mathematics behind the phenomenon.