Gowers has a few dozen short pieces of this sort, listed at http://www.dpmms.cam.ac.uk/~wtg10/mathsindex.html http://www.dpmms.cam.ac.uk/~wtg10/mathsindex.html.

Gowers has a few dozen short pieces of this sort, listed at http://www.dpmms.cam.ac.uk/~wtg10/mathsindex.html http://www.dpmms.cam.ac.uk/~wtg10/mathsindex.html. Another one that might be of interest is "why study finite-dimensional vector spaces in the abstract if they are all isomorphic to R^n?" (http://www.dpmms.cam.ac.uk/~wtg10/vspaces.html http://www.dpmms.cam.ac.uk/~wtg10/vspaces.html) The answer, roughly, is that the notation is less ugly if you don't have to keep track of coordinates, and that the abstract theory carries over better to the infinite-dimensional case.