Part of the beauty in the original equation is that it contains every object thought to be elemental in arithmetic and moreover, it contains every one of them exactly once.

It contains 0, 1, +, , ^, which are sufficient to express all of elementary natural arithmetics (unless I'm mistaken) -- all natural numbers can be expressed by adding enough ones to a zero (0, 0+1, 0+1+1, ...), and if I recall correctly, + and aren't enough to state all the truths in natural arithmetics so ^ is needed.

There is a very interesting paper on this called "The saga of the High School Identities" by S. Burris (http://www.math.uwaterloo.ca/~snburris/htdocs/MYWORKS/PREPRI...)

Moreover, it contains three very attractive (if not the most attractive) mathematical constants we know. There is so much we don't know about their relationship. We have no idea if any of these numbers is transcendental or not: pi + e, pi − e, pi*e, pi/e, pi^pi, e^e, pi^e. We don't even know if half of them are even irrational or not (therefore, we don't know if pi is just another facet of e, or maybe an entirely different object!)

So to see all this (and more; one could say so much more) in one equation so terse is so surreal a feeling.