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Riemann, following deep suspicions of Gauss that the Euclidean model is incorrect, sought to understand the shape of space.  At the turn of the twentieth century there was wide understanding among the physicists that geometry is fundamental to the description of nature.  Einstein’s gravitational equation makes the geometrization of gravity explicit with the Einstein tensor being composed purely of geometric elements (Ricci tensor, metric, scalar curvature) and the stress-energy tensor whose form is very similar to the second fundamental form terms of a hypersurface.  So for a century the centrality of geometry in description of nature was fundamental.  At the same time, the belief that it is right to model the universe as a flat three dimensional universe has not been fundamentally shaken.  This is why the Arnold book on Mathematical Methods in Classical Mechanics can clearly state this as a ground level empirical fact.  I believe that I have produced in 2008 the first clear argument that we have empirical evidence from the CBR temperature distribution regarding the compactness of the universe.  Once known to be compact, we essentially have a gigantic arsenal of geometric results  built up over the past century to address nature directly where global topology enters automatically rather than as exotic features of physics theories.  I have also shown that there is strong empirical evidence that the universe is a four-sphere of radius numerically equal to $1/h$ which provides an extremely simple and parsimonious connection between macroscopic and microscopic phenomena.