  In this paper, I shall demonstrate that sufficiently high-dimensional closed
positively-curved Riemannian manifolds are either diffeomorphic to a spherical
space form, or isometric to a locally compact rank one symmetric space. This
surprising classification of positively-curved Riemannian manifolds results
from combining the concentration of measures of Grassmanians with
Brendle-Schoen pointwise (weakly)- 1/4-pinching Theorem. A direct corollary of
the main result within this paper is the answering of the long standing Hopf
Conjecture in sufficiently high dimensions.
