Faltings' theorem is a significant result in number theory, proven by mathematician Gerd Faltings in 1983. It states that for a given algebraic curve defined over the rational numbers, there are only finitely many rational points on the curve, provided the curve has a genus greater than one. This means that complex curves, like elliptic curves, have limited solutions in whole numbers. The theorem has profound implications for the study of Diophantine equations, which are polynomial equations that seek integer solutions. It helps mathematicians understand the distribution of rational points and has connections to other areas, such as arithmetic geometry and modular forms.