One, Two, Three: Absolutely Elementary Mathematics

Math writer and teacher Berlinski is well-known for hid 1997 book A Tour of the Calculus. In this outing he reintroduces readers to their childhood friends, the integers, bringing out their complexity in a way elementary school teachers never did. For instance, he cites a book by the 19th-century German mathematician Richard Dedekind, whose title poses key questions about the nature of integers: "what should numbers be, and how should we think of them?" Berlinski devotes the book to exploring these questions, which are more vexing than they appear, if, as Bertrand Russell noted, numbers are neither objects nor properties of objects. Berlinski leads readers through basic operations like addition and multiplication, the development of set theory, and a cautious foray into the realm of negative numbers, but skirts any extensive discussion of counting systems based on numbers other than 10. The book is often a triumph of style over content; Berlinski's rhetorical flourishes amplify clumsy factual errors: for instance, Heidelberg was not "blasted to smithereens" in WWII. Many readers will be able to find other popular introductions to mathematics more to their liking. (May)