Why does volume concentrate near the boundary in high-dimensional spaces?

In high dimensions, most volume of a hypersphere lies near its surface, not its center.

As dimensionality increases, the ratio of inner volume to total volume shrinks exponentially. For a unit hypersphere, almost all points lie in a thin shell near the boundary. This breaks low-dimensional intuition and affects sampling, density estimation, and distance-based learning. The phenomenon is tied to exponential scaling of volume and surface area in n-dimensional geometry.