A biography I was perusing, ancillary to my graphic peregrinations emphasized something I didn't catch when I went to see the traveling Escher exhibit a few years ago. He considered himself to be quite poor at math, and apparently had difficulty following abstract, equation-oriented papers. Intuitively, though, and in terms of graphically working out sketches by hand he was brilliant. He grasped the bones of the math and clothed it in figures instead of formulas.
I think that touches me as strongly as it does because really, I love math. It's another way to describe how things relate to each other, and it does so in fascinating and breathtaking ways. However, I am very bad at the execution of mathematics. If you present me with a formula I am certain to pick it up by the wrong end, apply the wrong principles to it, and make a complete mess of things. I confuse orders of magnitude with depressing regularity. I was only able to finally understand what a function is when I thought of it in terms of what an RNA molecule does to a protein. So in a way I see Escher as a role model, in terms of being able to grasp and appreciate the essence, even though I fail at the mechanics. He's the friend who comes to the side door and sneaks me into the lecture hall of Mathematics, capital M.
To return to my earlier point, though - and his earlier work - I think part of what makes Escher's art as enduring as it is goes beyond its mathematical genius. There is a life to the line of his work that in some ways is more evident in his non-geometrical pieces - it is so easy to be drawn into the repetition, the metamorphosis, because of that inherent movement, yet that ease obscures its agent. Look at The First Day of the Creation, then try to find a better depiction of "the earth was without form, and void." Typing the words, it seems absurd - how do you draw a formless form? for a woodcut, no less. Or the snake in The Fall of Man - though I particularly like Eve's "dude, get over it!" expression and aspect as well. Castle in the Air shows up as a poster on occasion, but have you noticed the figure on the turtle? I could go on, but I'll stop after referring to two of my favorite, very simple early woodcuts: they are, of course, cats.