The Pleasures of Counting: A Book Review

ertion,” they considered their book to be popular in that it required only “a good high school course” by way of background. And it was a popular book. I remain very fond of it for reasons that are personal as well as objective. As a high school student I had access to numerous algebra and trigonometry books that those of a certain age and British Commonwealth lineage would associate with the style of Hall and Knight—unremitting drill, for those who have not shared the experience. But What Is Mathematics? was the only book in my high school library that suggested the depth of mathematics. Here was a book, after all, that discussed the Prime Number Theorem in the first chapter. I suspect that I am not the only one who learned from Courant and Robbins that the trees actually make up an interesting forest. For better and for worse, times do change. Certainly the direction of mathematics is constantly shifting as new fields find favor while others fall by the wayside. One might expect Courant and Robbins to choose their topics differently were they writing their book today. Linkages and Mascheroni compass constructions might be dispensed with, continued fractions and projective geometry curtailed. But an even more fundamental dynamic would necessitate another approach: a good high school course is not what it used to be. Reading the precise definition of continuity and then using it to prove the Intermediate and Extreme Value Theorems requires an intellectual discipline that is no longer within the proximate reach of the high school graduate. It is very difficult nowadays to imagine sending a good college freshman to Courant and Robbins to find out what The Pleasures of Counting