 Such geometries on surfaces spurred the development of three-dimensional and higher dimensional spaces with different curvatures: positive, null, and negative. An example of a space of positive constant curvature is the 3-sphere (also called hypersphere) used by Bernhard Riemann in his 1854 dissertation (see Riemann 1868; for an English translation see Riemann 2016). A 3-sphere is a surface in a four-dimensional space that is obtained as a generalization of the 2-sphere as visualized in three dimensions: in both cases we define the relevant notion as a locus of points that have a constant distance from a point (its center). For instance, the unit 2-sphere centered at the origin is the set of triples of real numbers \((x, y, z)\) that are one unit away from (0, 0, 0), i.e. that satisfy \(x^2 +y^2 +z^2 =1\), and the 3-sphere with distance 1 from the origin (0, 0, 0, 0) is the set of quadruples \((x, y, z, w)\) of real numbers satisfying \(x^2 +y^2 +z^2 +w^2 =1\). It is a model of physical space that is finite but unbounded, in explicit opposition to Newton’s conception of space.