Some branches of math seem to have reasoning which is more global. There is a lot of efficiency in the proofs because the reasoning transfers easily between proofs. For other branches of math, a lot of truths seem to be more local. The proofs tend to have lots of sub-cases and exceptions. There are fewer general principles. Does anybody know why branches of math vary like this? Can you place different branches of math on this scale from being dominated by more ad hoc to being dominated by less ad hoc proofs?



Why do branches of math vary in proof styles and what category are different branches in?
The only thing this reminds me of is [Tim Gowers's nice article](http://www.dpmms.cam.ac.uk/~wtg10/2cultures.ps) on the two cultures of mathematics, in which he compares and contrasts "geometry" (very broadly defined) and combinatorics.


The categories in the article don't exactly match up with the categories in the question, but perhaps there's some point of contact. 


