Poincare Conjecture

The Poincaré Conjecture deals with the types of possible three-dimensional spaces that can exist. Proposed by Henri Poincaré in 1904, it asks whether every simply connected, closed 3-manifold is equivalent to a three-dimensional sphere. In simpler terms, if a shape has no holes and is finite, can it always be transformed into a 3D sphere by just deforming it continuously? This question puzzled mathematicians for nearly a century, until Grigori Perelman provided a groundbreaking proof in the early 2000s using Ricci flow, a mathematical technique that reshapes spaces over time. His work earned him a Fields Medal—the highest honor in mathematics—which he famously declined.