Fifteen years ago, if publishers were sure of anything, it was that (1) calculus is not funny, and (1+1) no one wants to go to lie in bed clutching a book about the concept and history of integral and differential operators. Then along came the always audacious David Berlinski (his bio described him as “having a tendency to lose academic positions with what he himself describes as an embarrassing urgency”). A mathematician who is by trade a purveyor of proofs, Berlinski wrote A Tour of the Calculus, proving the skeptics wrong on both counts. With One, Two, Three: Absolutely Elementary Mathematics, Berlinski has now applied his vast knowledge, wit, and inimitable trademark writing style to tackle another subject about as sexy as American cheese: arithmetic. But don’t worry, you won’t find any multiplication tables here--this is a book about what it means to multiply (and add, subtract, and divide). Berlinski challenges us to see these as deeper issues, a level of mathematical thinking that most people never consider, but which forms the very logical foundation upon which rest ideas as vital as one plus one equals two.

Is there more to arithmetic than its application through our rote rules of calculation? Berlinski describes how, beginning in the late nineteenth century, mathematicians got around to questioning the meaning of arithmetic, and searching for axioms upon which that structure might be placed. Then he guides us through their reasoning.

Numbers form the foundation of our universe, yet most of us never puzzle over what they mean. We take for granted our numbers, the operations we perform on them, and the rules, such as commutivity, that those operations follow. It all seems to work when we buy our cappuccino and croissant, so why question it, unless you get shortchanged? The truth is, we don’t question arithmetic because we are in that famous and unenviable position of not knowing the extent of what we do not know. But Berlinski educates us, and shows that the logical basis of arithmetic is worth knowing, and worth appreciating, for it is both beautiful and profound, and represents a grand feat of human imagination. It is the revelation of a world of ideas upon which the simplest counting and calculating--acts without which no planning or transactions, from engineering to commerce, could exist--is predicated. That is David Berlinski’s gift to the reader. It is candy for the intellectually curious.