Exotic Spheres

In 1956, John Milnor astonished the mathematical community by discovering exotic spheres, i.e. smooth manifolds homeomorphic but not diffeomorphic to a standard sphere. Less than seven year later, exotic spheres in high dimensions were fully classified up to diffeomorphism by the work of Kervaire-Milnor, which gave birth to surgery theory. These important achievements have been possible thanks to great advances in differential topology, as well as in homotopy theory. This talk will survey those effervescent years in topology.