Mathematically Speaking is a dictionary of quotations about mathematics, arranged by topic. It is a book to thumb through and muse about -Jwhich is fortunate,, for otherwise it would be impossible to review. "Dictionaries," says the preface, quoting Samuel Johnson, "are like watches: the worst is better than none, and the best cannot be expected to go quite true." This is far from being the worst, but the authors are right: it does not quite go true.
There is existentialist soul-searching. "Ah! Why, ye Gods! Should two and two make four?" queried Alexander Pope. John von Neumann's answer: "In mathematics you don't understand things. You just get used to them."
There is philosophy disguised as frivolity. "The biologist thinks he is a chemist, the chemist thinks he is a physicist, the physicist thinks he is a God, and God thinks she is a mathematician." Or "1+1 = 3 for large values of 1." And there is genuine frivolity. "The wonderful thing about tensors, is tensors have traces and norms, their tops are made out of vectors, their bottoms are made out of formsI" There are pronouncements from the world of arts. "I tell them," said Thomas Mann, "that if they will occupy themselves with the study of mathematics they will find it the best remedy against the lust of the flesh." Never worked that way for me.
Nor for Roger Zelazny, who - in response to Edna St Vincent Millay's verse about Euclid - wrote:
"An ellipse is fine as far as it goes.
"But modesty, away!
"If I'm going to see Beauty without her clothes "Give me hyperbolas any old day."
And there are pearls of wisdom from the profession. Andre Weil:
"Mathematics has this peculiarity, that it is not understood by non-mathematicians." George Polya: "This principle is so perfectly general that no particular application of it is possible."
Imagine 362 pages of that - it palls if you read more than two pages at once. So what can I do to finish this review? Let's see if I'm in the book! Gosh, I am. Four quotes about mathematics, one on proof. But my joy rapidly becomes confined when I find I have been characterised in the index as a physicist. Moreover, two of my quotations are attributed to The Nature of Mathematics, not the title of any book I ever wrote. (Easily fixed: for "Nature" read "Problems".) Paul Hoffman is listed as "Hauffman", and Norbert Wiener is spelt that way on page 177 but "Weiner" on page 176. So the dictionary indeed does not go quite true.
These minor flaws aside, this is a valuable reference that belongs in most mathematical libraries. School libraries should not buy it unless they do not mind kids giggling over a few obscene, and unfunny, verses. If the editors check their information and delete the expletives, the second edition will be a veritable Rolex. Right now what they have given us is a Swatch.
Ian Stewart is professor of mathematics, University of Warwick.
Editor - C. C. Gaither and A. E. Cavazos-Gaither
ISBN - 0 7503 0503 7
Publisher - Institute of Physics Publishing
Price - £19.95
Pages - 484