Fourth, mathematicians have generally found that one of the most powerful ways of changing the viewpoint is through the “structural analysis of a problem”—that is, through breaking an overwhelming problem into small pieces. “Many proofs in mathematics have been actually found by extremely roundabout processes,” Shannon pointed out. “A man starts to prove this theorem and he finds that he wanders all over the map. He starts off and proves a good many results which don’t seem to be leading anywhere and then eventually ends up by the back door on the solution of the given problem.”
