What happens in the mind of the creator, the composer, when he creates, is still unknown. It is this "mystery" that this book aims to shed light on. Does artistic creation involve specific intellectual and biological processes? Can we get as close as possible to its mechanism to understand how a composer, a musician, a conductor, chooses to put together this and that note, to make this and that rhythm succeed one another, to bring out something new, to produce beauty, to arouse emotion? Is it possible to understand what happens in the composer's brain when he writes Le Sacre du printemps or Le Marteau sans maître ? Trying to build a neuroscience of art is the challenge of this book, which is the result of a debate between Jean-Pierre Changeux, the neurobiologist, who made the brain the main focus of his research, and Pierre Boulez, the composer, for whom the theoretical questions related to his art, music, have always been essential. A deeply new book. An intellectual event. Conductor, composer, founder of Ircam, Pierre Boulez is one of the greatest creators of the 20th century. Also a music theorist, he held the "Invention, Technique and Language" chair at the Collège de France for nearly twenty years. Honorary professor at the Collège de France, member of the Academy of Sciences, Jean-Pierre Changeux is one of the greatest contemporary neurobiologists. Philippe Manoury is a composer and professor emeritus at the University of California, San Diego.