Can anyone explain the Poincaré conjecture in simple terms?
OK This is tough stuff, and in reality, too toush to summarise in a paragraph but I’ll have a go. In topology, a sphere with a two-dimensional surface is essentially characterized by the fact that it is simply connected (In topology, a geometrical object or space is called simply connected if it is path-connected and every path between two points can be continuously transformed into every other. Informally, an object is simply connected if it consists of one piece and doesn’t have any “holes” that pass all the way through it. For example, neither a doughnut nor a coffee cup (with handle) is simply connected, but a hollow rubber ball is simply connected. In two dimensions, a circle is not simply connected, but a disk and a line are. Spaces that are not simply connected are called non–simply connected or, in a somewhat old-fashioned term, multiply connected.).. The Poincaré conjecture is that this is also true for spheres with three-dimensional surfaces. The question has been solved for
