My experience is that visuals help people _feel_ like they understand the concept, but the equations are necessary to get an _operational_ knowledge.
It's all well and good to be able to talk about the "deepest human knowledge" at a dinner party, but it doesn't help you solve actual problems using the fourier transform.
My brain works the opposite. Equations give me something I can work with but feels like voodoo, and I only get operational knowledge once I can visualize it in some way.
It's all well and good to be able to talk about the "deepest human knowledge" at a dinner party, but it doesn't help you solve actual problems using the fourier transform.