What are your mathematical gems? Which results or ideas in mathematics give you the greatest pleasure? Which of them would you choose to take with you to while away the hours on a desert island? Is there a mathematical book above all others that you would wish to have with you? How would you make your choices? And what would be the reason for each specific choice? Similar questions are asked of celebrities (and noncelebrities to boot) in a long-running and very popular radio programme in Britain called Desert Island Discs. The difference is that the radio guests are asked to choose a number of pieces of music, together with one book (other than the Bible or Shakespeare, which are routinely provided), and one luxury.