Despite the suspicion and distrust with which it is generally associated, ambiguity is in fact a useful, even valuable, quality in many fields. In mathematics – the science in which clearness and accuracy reign supreme – ambiguities provide the spark to finding solutions and shedding light on intuitive insights, and thus provide opportunities and incentives for progress. Something similar happens in literature and artistic creation, where ambiguity enhances beauty and aesthetic pleasure. The book explains the importance of this key concept, narrates episodes and events from the history of mathematics (such as: the Greeks’ bewilderment after having discovered incommensurability; non-Euclidean geometry; the infinite; and probability), examines a selection of literary examples drawn from Italo Calvino, Philip Roth and Herman Melville, and describes how literature and mathematics come together in the game of chess.

Gabriele Lolli teaches Philosophy of Mathematics at the Scuola Normale Superiore in Pisa, after having taught Mathematical Logic for many years at the University of Turin.