Only then will you truly grok Feynman's joke about mathematicians: "Mathematicians can only prove trivial theorems, because any theorem, once proved, is trivial."
(When I first read that at age fifteen or so, it was humor. Now it is dark humor. Still funny, of course, but with richer overtones.)
Only then will you understand how James Clerk Maxwell's life work can simultaneously be one of the top ten intellectual feats in the history of mankind and something that most undergraduate physics majors learn in a semester or two.
(I'm speaking from experience.)
But it is true that we routinely use the equations to solve problems that were very difficult intellectual struggles for Maxwell. A big problem is that Maxwell was encumbered by his mathematics and notation - everything he did was later refactored to be more straightforward. The dev, grad, curl stuff we use today came later. We have Oliver Heaviside - a man whose name is now more famous from Cats lyrics - to thank for them.
This. A thousand times this. It takes like three weeks of screwing around to get something remotely valuable, and oftentimes a summary takes just a paragraph that people look at and say, "Well, yeah, duh, that's obvious isn't it?"