How often does a memory lapse or an imperceptible delay in behaviour have dramatic consequences? This is what mathematicians call “chaos”, symbolized by the metaphor of the butterfly effect, introduced by the meteorologist Edward Lorenz to illustrate the instability of atmospheric movements: flapping butterfly wings can end up causing a storm. The ideal of a comprehensible, predictable universe crashes up against a shifting, chaotic, and apparently meaningless reality. Although equal causes may generate equal effects, similar causes do not necessarily lead to similar effects... on the contrary! This book tells the story of how mathematicians have identified chaos as a source of uncertainty and chance governing many natural and social systems. We know we will never be able to master them, but we can at least understand their dynamics and know which questions we can answer.

Marco Malvaldi is a chemist, a non-fiction writer and a popular mystery novelist.

Stefano Marmi teaches Dynamic Systems at the Scuola Normale Superiore in Pisa, where he heads the Ennio De Giorgi Mathematical Research Centre.