Carl E. Linderholm: Mathematics Made Difficult (1971)

Edition: Mosby-Wolfe, 1971 (Buy from Amazon)
Review number: 1083

When I was a mathematics graduate student, this book was passed around the department, delighting those of us working in pure mathematics. Basically, it takes apart the sort of mathematical ideas generally taken for granted, and shows that they are much more complicated than it first seems if you want to make them rigorous. (There is some cheating when ideas from category theory are introduced and make the explanations even more abstract than they need to be.)

There is, of course, a subject for a serious book in this; I can think of two without any effort (Rudy Rucker's Infinity and the Mind and the far older Bertrand Russell's Introduction to Mathematical Philosophy). Mathematics Made Difficult is not in any sense a book which aims to educate and inform its readers. Much of the mathematics is presented in a way which would probably not make a great deal of sense to anyone not already familiar with it (a course in the foundations of number theory is really the minimum needed to understand most of it, and one in category theory for the detail). What is enjoyable about Mathematics Made Difficult is that it is very funny, full of parodies of school textbook problems and bad puns. Mathematics is not easy to turn into humour, and this book is one of the very small number of consistently successful examples.