Doing the math

I'm sorry to keep harping on about this now but I have just had another sort of epiphany regarding math.

It seems to me that math has become the be-all and end-all of physics simply because making a mathematical approximation of something that works to n decimal places is deemed to be good enough.

Well, here's the thing. Schrodinger made a shitload of pretty math that describes electron orbitals. This math is fairly dense and difficult to understand. However, if you take a four dimensional figure with varying phase changes then you can exactly duplicate the result of those equations without ever having to resort to the pretty math. Which one is correct? The dense math because it looks cool if you can do it or the brute-force because it works?

I just wrote about fifteen lines of code that spits out graphical representations of electron orbitals and never goes near Schrodinger's equations.

Now then. When was the last time anyone actually saw an electron orbital in the flesh?

Atomic force microscopes are cool but they show little spheres.