Posted:

**Mar 09, 2011 2:53 pm**...though, in maths as opposed to physics, I think they often do. New, much more powerful ways of looking at things emerge, which throw out what used to be advanced and deep results almost as a by-product.

I once spent a semester (among other things) studying a slim volume called "Calculus on Manifolds", which started with that 19th century achievement, Stokes' Theorem, the high-water mark of calculus at the time, and by the time we got through to the final chapter, that theorem had become pretty much a trivial special case of the mathematical tools we had acquired during the course of the book.