[MUDDOG]

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

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

[Aurelius]

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

Late one night a policeman spots a slightly tipsy man bent over under a street light, looking for something. The policeman says "Have you lost something, sir ?" The man says "Yes, I lost my keys." The policeman say "Are you sure you lost them here?" The man says, "No, I lost them over there, (pointing into the dark) but the light is here."

[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)