John Milnor
fl. 1931, Orange, New Jersey, United States
TopologyGeometryAlgebraFields Medal 1962Abel Prize 2011
American mathematician who transformed differential topology, geometry, and dynamical systems through exotic spheres and classification theory.
John Milnor discovered exotic differentiable structures on spheres, showing that a topological sphere need not have the standard smooth structure. His work also introduced important ideas in Morse theory, geometric topology, and dynamical systems. He received the 1962 Fields Medal and the 2011 Abel Prize.
Workplaces: Stony Brook University
United States
Award-winning work
Fields Medal 1962The 1962 Fields Medal recognized Milnor's landmark contributions to differential topology, above all his 1956 discovery that the seven-dimensional sphere admits several mutually non-diffeomorphic differentiable structures — the exotic spheres. His construction founded the systematic study of smooth structures on manifolds and led, in joint work with Kervaire, to the classification of exotic spheres in higher dimensions. The citation also pointed to his proof that certain Lie groups admit no faithful finite-dimensional representation, and to the surgery-theoretic methods he pioneered, which became the principal tool for classifying high-dimensional manifolds.