Gerd Faltings proves in 1983, in Inventiones Mathematicae, the Mordell conjecture: every algebraic curve of genus greater than 1 defined over a number field has only finitely many rational points. The conjecture, formulated by Louis Mordell in 1922, had remained open for six decades, and its proof represents one of the greatest advances in 20th-century arithmetic geometry, introducing techniques — in particular the so-called Faltings height — that would become central tools of later number theory, including developments related to Fermat's Last Theorem. Faltings received the Fields Medal in 1986.