Theorem of the Poincaré conjecture

The Poincaré Conjecture, now a theorem proven by Grigori Perelman, states that any three-dimensional shape that is both closed (no edges or boundaries), simply connected (any loop can be shrunk to a point without leaving the shape), and topologically equivalent to a sphere, must actually be a sphere. In essence, if a 3D object has no holes and all parts are connected smoothly, then it is just a 3D sphere in disguise. This clarified understanding of 3D spaces helps mathematicians classify and understand the fundamental shape of our universe.