I love quotes. For years, I have collected them, used them in my email "signature" file, included them in assignments, and generally annoyed people with them. My collection includes many quotes about mathematics, which range for the insightful to the spectacularly wrong-headed. (After all, as John Kenneth Galbraith once pointed out, "If all else fails, immortality can always be assured by spectacular error.") I'm happy to welcome Mathematically Speaking to my shelves.
The authors have put together a "dictionary of quotations" about mathematics in fairly standard format, which includes (thank goodness) a proper set of indices. Those indices alone mean that this book surpasses by far the competition. Memorabilia Mathematica and Out of the Mouths of Mathematicians are both useful collections, and 777 Mathematical Conversation Starters is fun, but when you're looking for a partly-remembered quote none of them is as easy to use as this book. In addition, the authors of Mathematically Speaking have tried to find precise sources for all their quotes. A bit too often, they give up and simply say "quoted by X in Y", but even then they still give Y as precisely as they can. Still, in these days of the internet and its free-ranging quotes, it's good to have even such "quoted by" sources indicated.
A lot depends, of course, on the authors' taste: they have to decide what quotes are worth quoting. Gaither and Cavazos-Gaither are pretty good, though the inevitable clinkers do get in. I'm not sure, for example, what Alan Turing meant by "Science is a differential equation. Religion is a boundary condition." Or what "The Cartesian criterion of truth" (that's the whole quote), by Unknown, source unknown, is doing here.
The authors describe their choices saying "Some of the quotations are profound, others are wise, some are witty, but none are frivolous." Well, too bad, I say. The frivolous ones are sometimes the best. The book does have a certain earnestness to it, though it includes Mae West's remark that "A figure with curves always offers a lot of interesting angles." (That's not frivolous?) Overall, the quotes are well chosen, and several are new to me. I'm glad to have the book. I think most of the readers of MAA Reviews would enjoy it too.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages. He somehow finds time to also be the editor of MAA Reviews.