The case of 3-manifolds that should be spherical has been slower, but provided the spark needed for Richard S. Hamilton to develop his Ricci flow. In 1982, Hamilton showed that given a closed 3-manifold with a metric of positive Ricci curvature, the Ricci flow would collapse the manifold to a point in finite time, which proves the geometrization conjecture for this case as the metric becomes "almost round" just before the collapse. He later developed a program to prove the geometrization conjecture by Ricci flow with surgery. The idea is that the Ricci flow will in general produce singularities, but one may be able to continue the Ricci flow past the singularity by using surgery to change the topology of the manifold. Roughly speaking, the Ricci flow contracts positive curvature regions and expands negative curvature regions, so it should kill off the pieces of the manifold with the "positive curvature" geometries S3 and S2 × R, while what is left at large times should have a thick-thin decomposition into a "thick" piece with hyperbolic geometry and a "thin" graph manifold.