 Archytas’s argument (in section   1  above), which conflated unboundedness with infinitude, could finally be put to rest. Riemann’s model allows for the universe to be finite and unbounded at the same time. In 1854 he wrote: “The unboundedness of space possesses in this way a greater empirical certainty than any external experience. But its infinite extent by no means follows from this; on the other hand if we assume independence of bodies from position, and therefore ascribe to space constant curvature, it must necessarily be finite provided this curvature has ever so small a positive value. If we prolong all the geodesics starting in a given surface-element, we should obtain an unbounded surface of constant curvature, i.e., a surface which in a flat manifoldness of three dimensions would take the form of a sphere, and consequently be finite.” (Riemann 2016: 39)