Erdős was born in Hungary in 1913 and died – at a maths conference of all places – in 1996, but for much of his life he had no fixed abode. With the rise of Nazism in Europe, he left Hungary in 1938 for the US, but in the 1950s and 60s was denied entry to the US for his links to communist sympathisers. Instead, he travelled from place to place with a suitcase, turning up at a mathematician’s door and declaring “My brain is open”. The unspoken deal Erdős offered was that his host would house, feed and generally care for him for a few days, and in return they would receive the chance to collaborate on some world-class mathematics.