Except that you'd get rather unintuitive results: recursion seems to tie nicely to algebra, while iteration seems to tie nicely to analysis (algebra: see grou

Except that you'd get rather unintuitive results: recursion seems to tie nicely to algebra, while iteration seems to tie nicely to analysis (algebra: see group actions, modules, lattice decompositions, analysis: many proofs require chaining inequalities together). But recursion is generally associated with functional languages/LISP/etc., while iteration is much more associated with traditional OO languages (and objects are pretty algebraic, the author gets that right). I'd say it's probably more dynamic typing versus static typing. Dynamic typing matches up very well with the sort of fuzzy proofs that occur in analysis ("well this is less than that, and that is less than the other, so this is less than the other by a little bit" seems close to "quacks like a duck"), and static typing seems very much like an algebraic idea. But, as someone working on a math masters, I can say that I prefer analysis and really like dynamically typed languages, so this might just be my pet theory of matching the world to myself.