Why is Maxwell's theory so hard to understand? (2007) [pdf]
I actually have happened to delved quite a bit to "really" understand the Maxwell's equations. I've bought original treatise, books with its commentary and plain old "for idiots" sort of books. His original treatise is super dense and unapproachable. Right now we can wear Maxwell's equations on t-shirt but their original form were forbidding. Even with modern form you "really" need to get concepts of differential geometry if you want to just play beyond abstract. There are tons of hand wavy explanations of div and curl out there but almost all can be broken with crafting clever question like “ok, so what you think curl of that would look like?”. I don't think even today I can claim I really get these concepts.<p>In any case, some of my biggest takeaways were these:<p>1. There is no such thing as "proof" of Maxwell's equations. Just like Einstein's field equations, Newton's laws and many other things in Physics, Maxwell equations are also simply laid out as <i>lets assume these</i>. Vast majority of “greatness” in Physics is simply assuming something without needing to fully understand it and then cross your fingers to see if some good predictions comes out of it.<p>2. The major achievement of Maxwell's equations is that you can predict velocity of light using other physical constants that have seemingly nothing to do with light. A consequence that we only later realized was that this was literally a constant and not relative to who is measuring it! This is easily one of the most non-obvious achievement in Physics.