 Riemann’s ideas were both profound and naïve, and for that reason they proved difficult to make precise, but we can content ourselves with being naïve initially. He supposed he was given a space (he called it a ‘manifold’) in which one can at any point impose a coordinate system at least on all points near to an arbitrary initial point, and if \(n\) numbers are needed to specify the location of a point he said that the space is \(n\)-dimensional. We can think of this process as providing a map of at least that part of the space near the initial point onto \(\mathbb{R}^n\). Riemann was very aware of the difference between local and global determinations, and this became one of the keys to his new ideas: the same local conditions are compatible with numerous different global configurations.