The important part is understanding the concept.. not to necessarily visualize it. For instance, once you understand the concept in 1D, it's not that much more difficult to extrapolate to multiple dimensions.
In my experience, it’s the transition from 1d to 2d that’s the most important. You learn the concept in 1d, then carefully transition to 2d while still keeping an eye on the 1d case and on what the extra dimension contributes. The understanding of the latter helps to get from n to n+1.
