Serre's conjecture

Serre's conjecture is a mathematical idea suggesting a deep connection between two concepts in number theory: modular forms, which are special kinds of symmetrical functions, and Galois representations, which describe symmetries of solutions to polynomial equations. It predicts that every certain type of Galois representation can be associated with a modular form, meaning these abstract symmetries can be understood through more concrete, well-studied functions. This conjecture bridges complex algebraic structures and analytic functions, providing a unified framework that enhances our understanding of prime numbers, equations, and symmetry in mathematics.