One might expect a book whose most recent edition was prepared nearly fifty years ago to seem old-fashioned, its terminology dated, its viewpoint out of line with current fashions. Its emphasis on problem-solving is up to date, and its choice of material has lasted so well that not a single word or symbol had to be deleted from this new edition. No, the book has worn well because although mathematics is still growing, it is the sort of subject in which old discoveries seldom become obsolete. But then it was never proved in the first place. However, new viewpoints can often render old proofs obsolete, or old facts no longer interesting.
Formal mathematics is like spelling and grammars matter of the correct application of local rules.
Meaningful mathematics is like journalism-it tells an interesting story. Unlike some journalism, the story has to be true. The best mathematics is like literature-it brings a story to life before your eyes and involves you in it, intellectually and emotionally. The main purpose of the new chapter is to bring Courant and Robins stories up to date-for example, to describe proofs of the Four Color Theorem and Ferrnat's Last Theorem. These were major open problems when Courant and Robbins wrote their masterpiece, but they have since been solved.