Exotic spheres are a type of mathematical object in the field of topology, specifically in the study of manifolds. They are variations of the standard sphere that have different properties, yet still resemble a sphere in many ways. Exotic spheres can exist in higher dimensions and are often used to explore complex concepts in geometry and algebra. The existence of exotic spheres was first proven by mathematician John Milnor in the 1950s. He showed that there are multiple distinct smooth structures on spheres in dimensions greater than four, meaning that these exotic spheres cannot be transformed into one another through smooth deformations. This discovery has significant implications in the study of differential topology and the understanding of manifold structures.