As someone who never took much advanced math or physics in school and really doesn't understand what either representation of that material is staying, personal

As someone who never took much advanced math or physics in school and really doesn't understand what either representation of that material is staying, personally I find the second example far, far more approachable because it is far more googleable! If Gauge Theory is a concept required to relate to the other content in that sentence I've got no shot of knowing gauge theory is involved in the first example. I don't know what the arrow between P and M means. I'd have to look up what a G-bundle is. Its basically not clear to me which parts are syntax and which are proper nouns. The example which reads more like prose than an equation expressed in terms of English words gives me much, much more context for where to begin reading about what I don't know.