In 1982, Richard Hamilton proved that a smooth closed 3-manifold admitting a metric with strictly positive Ricci curvature is a spherical space form (in particular such a manifold which is simply connected is $S^3$). This led to a (by all accounts still active) research program culminating in Grigori Perelman's proof of Thurston's geometrization conjecture in 2006 (and hence the Poincare conjecture).