Every picture I've seen to illustrate wormholes is always a shortcut from one point on a 2D surface to another. And it's easy to see that the distance is shorter through the wormhole since we are view it from a 3D perspective. This makes me wonder if higher dimensions are required to construct wormholes. It seems the wormhole must travel through the higher dimension in order to create a shorter distance through the regular space. Do wormholes need higher dimensions to exist?