John Willard Milnor
Milnor and seven-dimensional spheres are virtually synonymous amongst mathematicians.
Milnor is recognized for his accomplishments in many fields of mathematics but perhaps he is best known for showing differentiable structures exist on exotic 7-spheres. He distinguished between these 28 structures by using numerical invariants. This work opened a new field of differential topology where one investigates properties of geometry preserved by continuous transformation.
Much of his life has been at Princeton University but currently he is Co-Director, Institute for Mathematical Sciences at Stony Brook, SUNY.