The Poincaré Conjecture and Grigori Perelman

The Poincaré conjecture (1904) stated that any simply connected, closed 3‑manifold is homeomorphic to a 3‑sphere. Simply connected means any loop can be contracted to a point. Perelman proved it in 2003 using Ricci flow (a geometric evolution equation). He refused the Fields Medal (2006) and the $1 million Millennium Prize (2010), saying he was no longer part of the mathematical community. He now lives in seclusion in St Petersburg. The proof filled three arXiv papers, later verified by several teams.