Langlands correspondence is a deep and influential concept in mathematics that connects number theory and representation theory. It establishes a relationship between Galois groups, which are used to study polynomial equations, and automorphic forms, which are functions that have symmetry properties related to certain algebraic structures. This correspondence suggests that for every L-function, a type of complex function important in number theory, there exists a corresponding automorphic representation. This relationship helps mathematicians understand the properties of numbers and shapes in a unified way, leading to significant advancements in both fields.