Poincaré Conjecture In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense), where a three-sphere is simply a generalization of the usual sphere to one dimension higher. In layman terms, the conjecture says that the three-sphere is the only type of bounded three-dimensional space possible that contains no holes. It was proved by a Russian Mathematician Grigori Perelman, but rejected the $1 million prize that came with it.