"A mathematician needs functions for the same reason that a builder needs hammers and drills. Tools transform things. So do functions. In fact, mathematicians often refer to them as "transformations" because of this. But instead of wood or steel, functions pound away on numbers and shapes and, sometimes, even on other functions."
"Brian Hayes explores this problem in the title essay of his recent book, "Group Theory in the Bedroom." Double entendres aside, the "group" in question here is a collection of mathematical actions - all the possible ways you could flip, rotate or overturn the mattress so that it still fits neatly on the bed frame."