Although it is often attributed to Hamilton, he has observed that Yau is responsible for the insight that a precise understanding of the failure of convergence for Hamilton's differential equation could suffice to prove the existence of the relevant spheres and tori in Thurston's conjecture. This insight stimulated Hamilton's further research in the 1990s on singularities of the Ricci flow, and culminated with Grigori Perelman's preprints on the problem in 2002 and 2003. The geometrization conjecture is now commonly recognized as having been resolved through the work of Hamilton and Perelman.