[PaulHoule]

The fact that you can write it in one equation shows that the theory is very simple because it is an expression of symmetry. E and B are not these two different things related by an inscrutable cross product but just two aspects of the same thing.

[scotty79]

You could write all physics in a single simple equation. deltaW=0 Where deltaW is deviation of the universe from the relevant math.

Writing Maxwell's as 1 equation or 4 or more is just esthetic choice where you decide what to accentuate.

20 might be too much because three dimensions are not really different from each other so the notation that maps over them wholesale is probably a good idea.

4 equations seem perfect if you want to differentiate between classical effects of the electric field and relativistic effects (magnetism).

I don't know if single equation really shows that they really have the same source and the relativity is involved or is it just a matrix mashup of the 4 separate equations that doesn't really provide any insights.

[toth]

It's true that you can always define notation to combine all equations you want into one. This means that, by itself, the observation that you can write Maxwell's equations as a single equation doesn't say anything very meaningful.

However, the notation that lets you do this in this specific case is very natural and not specific to Maxwell's equations. Differential forms are very natural objects in differential geometry, mathematicians would have likely introduced them and studied without inspiration from physics. The fact that Maxwell's equations are very simple in this natural geometrical language does say something meaningful about their nature and elegance, I think.