The Mordell conjecture is a mathematical hypothesis proposed by the mathematician David Mordell in 1922. It states that for any algebraic curve of genus greater than one defined over the rational numbers, the set of rational points on the curve is finite. This means that there are only a limited number of solutions in rational numbers for such curves. The conjecture is significant in the field of number theory and has implications for understanding the distribution of rational points on curves. It was proven in 1983 by Gerd Faltings, leading to the result now known as Faltings' theorem, which confirmed the conjecture's validity.