I'm not sure where this goes; sorry if I placed it in the wrong category.
I just got through Stokes' Theorem in Calculus 3 recently, and the professor showed the the Fundamental Theorem of Calculus, Green's Theorem, and other such theorems are merely special cases of Stokes' thoerem. He showed this through the use of differential forms, which are apparently in differential geometry and beyond the scope of my understanding.
So, I got to wondering. Is there a theorem that encompasses multiple mathematical fields similar to Stokes' theorem? For now, I'm calling it "The Fundamental Theorem of Mathematics". I'm wondering if such a theorem exists where the field of calculus (and/or other fields of mathematics) is merely a special case of some mathematical theorem. Does such a theorem exist? If so, Where can I read up on this theorem? Any information about theories regarding such a theorem is also helpful.
I checked Google and didn't find much. There's something about the foundation of mathematics, but I couldn't find many details.
Less importantly, I wonder if there's another level for sciences, where 'mathematics' is a special case of a certain formula or principle. Or, to go to a ridiculous level, the laws governing our universe are a special case of a certain principle or formula.
Thank you!