Donaldson (1983) showed there exists an exotic smooth Differential Structure on . Donaldson's result has been extended to there being precisely a Continuum of nondiffeomorphic Differential Structures on .
See also Exotic Sphere
References
Donaldson, S. K. ``Self-Dual Connections and the Topology of Smooth 4-Manifold.'' Bull. Amer. Math. Soc. 8, 81-83, 1983.
Monastyrsky, M. Modern Mathematics in the Light of the Fields Medals. Wellesley, MA: A. K. Peters, 1997.