The Kervaire-Milnor theorem is a significant result in the field of topology, particularly in the study of high-dimensional manifolds. It states that there are only specific dimensions in which a certain type of manifold, known as a smooth manifold, can be constructed. Specifically, it identifies the dimensions in which the existence of exotic spheres is possible, which are spheres that are homeomorphic but not diffeomorphic to the standard sphere. This theorem was proven by mathematicians Michel Kervaire and John Milnor in the 1960s. Their work has implications for understanding the structure of manifolds and the classification of differentiable structures in various dimensions. The theorem highlights the intricate relationship between topology and geometry in higher dimensions.