This notion of "analogy" is formalized in category theory. At times this is done to great effect --- the generalizing power of category theory can help a mathe

This notion of "analogy" is formalized in category theory. At times this is done to great effect --- the generalizing power of category theory can help a mathematician see the forest for the trees. This has been done to great effect, e.g., in programming language theory. Then again, at times category theory is shallow, nothing more than abstract nonsense. (N.B. this is a technical term.) The strict formalist in me likes category theory because it has so many names for things, many of which are in Greek. The intuitionist in me thinks the field is pointless but likes drawings with arrows in them. All in all, it's a win-win. :)