The Langlands program is a set of interconnected ideas in mathematics that aims to link number theory and representation theory. It proposes deep relationships between different areas, such as algebraic geometry, modular forms, and Galois representations. At its core, the program seeks to understand how solutions to polynomial equations relate to symmetries and how these symmetries can be represented in various mathematical structures. This has led to significant advancements in both theoretical mathematics and practical applications, influencing fields like cryptography and mathematical physics.