Abstract

In 2003, Grigory Perelman proved the celebrated Poincaré conjecture, establishing that the simplest topological property characterizes the simplest closed three-manifold. The paper discusses the unexpected irony whereby techniques from analysis and mathematical physics to which topology had contributed so much, would one century later repay the favor by being used to solve the most famous purely topological problem of all time. Few would have imagined that the object central to Perelman’s proof, a hierarchy of Riemannian manifolds connected by the Ricci flow, might provide a mathematical object useful for modeling space and space-time at different scales.