And the best part is, this sort of "visual math" is applicable to every single field of mathematics; by visualizing every equation you come across, you'll find

And the best part is, this sort of "visual math" is applicable to every single field of mathematics; by visualizing every equation you come across, you'll find that you eventually gain a crisp (and often intuitive) understanding of the math. Not every math field uses equations, and most of those that do, use equation, where terms are very far from being ordinary (integer, real, complex) numbers, and picturing a rectangle when you have xy will only mislead you. For instance, sometimes xy is not equal to yx, sometimes x and y are not 0, but xy is 0. Of course, there are other ways to employ visual intuition to gain better understanding of the problem -- for instance, if our multiplication comes from group structure, we can imagine an object the symmetries of which are group elements. Nevertheless, the history of mathematics teaches us that the greatest thing started to happen when we ditched our geometric and intuitive understanding of math and turned to more formal ways. I'm certainly happy to see a geometric interpretation of some definition, theorem, or proof, but I'm more interested in logical argumentation than appealing to intuition.