[abelaer]

(Disclaimer: haven't read the whole thing) This just seems like one of these situations: https://xkcd.com/927/

The fact that the same physical system can be described by very different kinds of mathematics is often very illuminating and interesting, rather than confusing. It's one of the reasons that physics can inspire mathematics, rather than maths just being a tool that physicists use. Different types of mathematics often allow you to emphasise different properties of the same system, so being comfortable in more than one language brings you freedom and new insights.

[zentiggr]

I've never had a chance to dive deeply into most 'advanced' math topics, but I've readd more than one of Hestenes's papers (and cohorts) and honestly GA looks to be so much clearer, concise, and more easily worked than having to blend together vectors, matrixes, and other constructs in order to do the same work in more complicated ways, with extra notational layers.

Again, I don't use any of this in real life, so YMMV, but it looks very clean, fast, and intuitive compared to (waves at everything else).