While it's neat to write them all as one equation, I disagree that it's an enlightening perspective to learn. While it seems like writing Maxwell's equations in one equation instead of two is a step forward with even more symmetry, what is actually going on is that you are obscuring the most important part of Maxwell's equations: the gauge structure. Without this, it actually becomes much more hidden just how geometric electromagnetism is.

When you write Maxwell's equations as the pair `dF = 0`, `d*F = J`, the first of those two equations is exactly what tells you that this is a gauge theory, and thus may write `F = dA` where `A` is a vector potential. This vector potential then becomes the connection which defines a covariant derivative in a fibre bundle, and one then sees that charged particles follow geodesics now in spacetime, but in an enclosing fibre bundle. This is foundationally important to modern physics, and IMO obscured by writing Maxwell's equations as `∇F = J`

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n.b. I'm not a particularly big fan of differential forms either, I think it leaves a lot to be desired, and it's super awkward to constantly have to pull out Hodge Duals every time you want to do something that involves the metric, but I'm also unconvinced that geometric algebra is the answer here.

However, from the perspective of Yang-Mills theory, that's rather questionable as you're stitching together the Bianchi identity and the Yang-Mills equation for no particular reason.

As opposed to the weird GA form it actually makes the physically most meaningful symmetry (Lorentz transformations) explicit. That's why it's actually used in Physics.

Anti symmetric space time tensors are the absolute standard. Further formulations that reveal other aspects, dualities, symmetries are much more niche and specialized subjects and not how the subject should be taught when first encountering it.

https://en.wikipedia.org/wiki/Covariant_formulation_of_class...