Thurston's geometrization conjecture is a far-reaching generalization of the uniformization theorem for surfaces, proposing that every compact 3-manifold can be decomposed into pieces that each have one of eight types of geometric structures. This conjecture, proven by Grigori Perelman in the early 2000s using Ricci flow with surgery, revolutionized the field of 3-dimensional topology and earned Perelman the Fields Medal, which he famously declined.