Laurent Lafforgue completes in 2002, after more than six years of continuous work, the proof of the Langlands program for the general linear group GL(n) over function fields, extending to arbitrary dimension the GL(2) case that Vladimir Drinfeld (Fields Medal 1990) had solved in 1974. The result, of extraordinary technical complexity, establishes a deep correspondence between automorphic representations and Galois representations in this arithmetic setting, consolidating one of the most ambitious lines of research in late-20th-century arithmetic geometry. Lafforgue received the Fields Medal in 2002.