[nine_k]

Humans have a limited capacity of holding something before their "mind's eye", like 5-7 items. The simpler the equation is, the easier it is to understand and operate. Of course, it only works provided that the parts of the equation are well-understood, too.

This way, the nabla symbol is very helpful in turning a group of (usually) 3 related PDEs into one pretty understandable one. Same for vector and matrix forms of common 2D and 3D transforms. Once you understand how these symbols work (they have a very regular structure), you can think at a bit higher level, and juggle with transforms that won't fit in your head in the scalar form, requiring toilsome operations on paper (or equivalent).

Say, general relativity is hard as it is; without various notational tricks which abstract away some complexity, it would likely be completely unwieldy.

A change of notation is like a refactoring in programming: a good set of powerful and well-defined functions makes the code to solve a problem significantly easier to produce and to understand, and harder to make an error.

[staunton]

Yes, good notation helps dealing with complexity. My point was that "number of equations" involved in a model or theory is not an objective measure of, really, anything.

Every system of equations can be written as "A = 0" for a suitable definition of A. That doesn't make it simple.