I wonder why so many people are under the impression that the notation is what is keeping them away and if only the notation was easier then the underlying concepts would be clear. For example, if you don't know what the pullback of a differential form is, it doesn't matter if I write it in clear text or if I write the common notation φ^* ω.

> It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else.

It's a domain reserved for people who want to learn it, and there's ton of resources to learn it. Expecting to understand it without learning it does not make any sense.