[KayEyeDoubleDee]

Now, I'm curious about the history of something like Maxwell's Equations vs Stokes' Theorem (or Green's Theorem, if that special case was discovered first)

Slick, do you have any insight (or reference literature) here?

[tq]So how come we first "invent" an area of mathematics and only subsequently "discover" that it describers Nature?

[mud]You are correct sir, e.g., tensor analysis for general relativity, and functional analysis for quantum mechanics.

If you go back through a few posts you'll see that TopQuark, in particular, would argue (i think) that most physical phenomena are explained in terms of existing mathematics. I naively suggested he might have it backwards, that usually the mathematics are constructed to explain the physical process, but I think he may have a point. The example of Newton and his version of calculus clouded my vision at first...

[MUDDOG]

I naively suggested he might have it backwards, that usually the mathematics are constructed to explain the physical process

There's an interplay between math and physics, so it's like what came first, the chicken or the egg.

In the case of general relativity, Einstein was floundering around for how to mathematize it until he happened upon tensor analysis. Same thing for quantum mechanics; the Hilbert space was there first, and turned out to be an excellent fit.

Sometimes it goes the other way, e.g., physics first, as with Newton and Fourier.