What Is a Manifold?

Standing in the middle of a field, we can easily forget that we live on a round planet. We’re so small in comparison to the Earth that from our point of view, it looks flat. The world is full of such shapes — ones that look flat to an ant living on them, even though they might have a more complicated global structure. Mathematicians call these shapes manifolds. Introduced by Bernhard Riemann in… Source