If you think of a landscape of plains, hills, and mountains, the curvature R of the surface is zero in the plains, which are flat—“without curvature”—and different from zero where there are valleys and hills; it is at its maximum where there are pointed peaks of mountains, that is to say, where the ground is least flat, or most “curved.” Using Riemann’s theory, it is possible to describe the shape of curved spaces in three or four dimensions.
