Philip Ball tells the story of how Kepler became a key figure in the scientific revolution of the 17th Century. He was a precocious mathematician who became an adviser to Emperor Rudolf II in 1600. Although he contributed to the idea that the sun, not the earth, was the centre of the solar system, his role at the court was to be an astrologer.

Philip brings the story of the shape of the snowflakes up to date. It was only 20 years ago with the development of the maths of fractals that we got to understand the formation of the myriad patterns of snowflakes.