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Mathematically Speaking

Times Higher Education Supplement July 1998

Mathematically Speaking is a dictionary of quotations about mathematics, arranged by topic. It is a book to thumb through and muse about-which 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 trace and norms, their tops are made out of vectors, their bottoms are made out of forms..."

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 that 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 spelled 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

Choice Volume 36, Number 5, 1999

Gaither and Cavazos-Gaither, compilers of books of quotations in statistics and physics, now offer one in mathematics, all with the same publisher. The authors have degrees in psychology, criminal justice, mathematical statistics and telecommunications, but neither is currently employed in mathematics, statistics, or physics. Their book consists of well over 1,000 quotations gleaned from some 800 publications, including scientific publications or historical note, 20th-century books and journals in mathematics, works of fiction (e.g., Alice in Wonderland, Sherlock Holmes, Shakespeare), and works by standard authors (e.g., Plato, John Dewey, Bertrand Russell). The source bibliography lists the works. The quotations are grouped by broad subject, and there are detailed indexes of subjects and authors. The collection of quotations is eclectic, ranging from the sublime to the silly (e.g., "Math was always my worst subject"). Several quotations have been extracted from some sources (e.g., six from Bertrand Russell's Mysticism and Logic and Other Essays). The lack of selectivity weakens the quality of the volume. Recommended only for libraries developing an extensive collection of mathematics reference sources.

T.G. Kirk Earlham College

Zentralblatt fur Mathematik Number 902, 1999

Logico-mathematical dictionaries often serve the useful purposes of a valuable teaching resource and a historical motivator of our students. We must answer every student's question and then ask several others of ourselves and our students. Dictionaries of quotations by leading mathematicians and logicians help us to do this difficult task. Further, they (sometimes) give us subtle hints for the new directions for research, which can give rise to ideas for intellectual discussion or even whole books.

The Dictionary is divided into 120 major topics such as, e.g., abstraction, algebra, calculus, computers, dimension, irrationals, logic, ordinals, perfect number, recursion, relations, set, tensor, topology, and vector. This occupies 362 pages! There are approximately 650 quoted authors several of which are not mathematicians. Among the quoted authors are Abel, Banach, Dehn, Dirac, Euler, Gauss, Goethe, Hardy, Heisenberg, Hilbert, Jacobi, Klein, Minkowski, Poincare, Wiener and Weierstrass. The quotations are in English or English translation. Three useful aspects of the dictionary are a massive bibliography, a comprehensive subject (by author) index and an extensive author (by subject) index. Future editions should include quotations from Paul Erdos (e.g., his slogan "Conjecture and Prove" or his several classes of unsolved problems that might help set the mathematical tone for the 21st Century). In a couple of places, the entries are for the same author with the name misspelt. A careful reading of page 247 will surprise the reader!

In conclusion, I highly recommend the dictionary to students, teachers and the intelligent general readers. Versions of the dictionary with entries in other languages would seem appropriate.

A.A. Mullin (Huntsville)

PASS MATHS May, 1999

Every so often, it's nice to have a quotation - whether it's to impress someone with your erudition (look it up) and wide literary knowledge, to head a chapter in a textbook someone's asked you to write, or simply to stick on your office/bedroom door to explain your attitude to life/amuse people/tell them you're not at home. You can get through life without quotations, but it's often more fun to use them.

The use of apt quotations can also be a way of establishing a coterie (the dictionary's on the third shelf - right hand end) of like-minded people. For example, devotees of the Hitchhiker's Guide to the Galaxy will use the terms "Forty-two", "out to lunch" and "Life? - don't talk to me about life!" with confidence and a slight smile, knowing that a fair proportion of the audience will enjoy it and understand what they mean. Actually, I'm not sure I've punctuated that last one correctly - I'll have to look it up.

Quotations can also frustrate. You've heard it. You like it - but where did it come from? Mathematically Speaking is a dictionary of quotations about mathematics, ably selected and arranged by C.C. Gaither and A.E. Cavazos-Gaither. As a bonus, it's got some nice cartoons in it as well.
The Chapters are arranged in alphabetical order by topic; for example Discovery is followed by Divergence, Division, then "e". You can use it to look up a quotation on a particular subject, or you can browse and enjoy.

It's even fun for non-mathematicians. I know, because I showed it to my wife - a proud non-mathematician - and she laughed out loud several times, then turned to the index and was pleased to find that Tom Lehrer had three entries, Lewis Carroll fourteen entries and Douglas Adams two. And she liked the one about the polar bear on page 353.

Mike Pearson

Crux Mathematicorum with Mathematical Mahem March, 1999

The book contains hundreds of quotations from hundreds of authors, as well as many apocryphal quotations from persons unknown. The quotations are grouped into 199 sets, ordered by topics, running from ABSTRACTION to ZERO. Most sections are just a few pages long, except for the topics MATHEMATICIAN and MATHEMATICS which have 29 and 80 pages respectively.

Also included is a complete bibliography of the source material plus two excellent indices, the SUBJECT BY AUTHOR INDEX and the AUTHOR BY SUBJECT INDEX.

The quotations vary from the profound to the witty. There are quotations from plays, and quite a few in poetry, including several mnemonics for pi. Unfortunately, this reviewer's favorite is missing!
How I want a drink 3.1415
Alcoholic of course 926
After the heavy lectures 5358
Involving decimal fractions 979

(Engineers can substitute "quantum mechanics" for "decimal fractions".)

The authors quoted come from all different walks of life, from professional mathematicians and scientists to historians, journalists, philosophers, poets, rap artists and writers. Some are famous, their names being almost household words: others are much less known. As might be expected, by far the majority of the quotations come from mathematicians and scientists.

To give a flavour of this book, here is a selection of some of the shorter quotations:

Some quotations from famous mathematicians

Richard Guy

Mathematics often owes more to those who ask questions than to those who answer them.

Paul Halmos

The only way to learn mathematics is to do mathematics

Leopold Kronecker

Number theorists are like lotus-eaters -- having once tasted of this food, they can never give it up.

George Polya

Geometry is the art of correct reasoning on incorrect figures.

Some quotations from others


I write thymes with addition and algebra, mental geometry.

G.K. Chesterton

Poets, do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom.

This book is a wonderful compendium and a great source of useful wisdom for teachers of mathematics. It is very readable, and, once one has started to read it, very difficult to put down.

Bruce Showyer
Memorial University of Newfoundland

American Reference Books Annual 1999

This witty, quite straightforward compendium of quotations in the area of mathematics may be just the right solution for speakers trying to find a quotation to flavor a speech. It is a useful source for students, professors, and public speakers who love to quote and to quote correctly.

This dictionary includes sayings by famous people ranging from Pythagoras to Ice-T (rapper). One can easily identify the author of the quotation. The book lists familiar and less well-known quotations. Bill Gates is quoted in the section entitled "Subtraction."

Sources such as The Complete Essays & Other writings of Ralph Waldo Emerson and the Complete Works of Lewis Carroll: Through the Looking Glass are quoted prolifically. For the most part, the sources are named. Subjects are arranged alphabetically. A quotation for a given subject may be found by looking for that subject in the alphabetic arrangement of the book itself. For example, there are nine quotations listed under the heading "PI." There is a subject by author index and an author by subject index.

The cartoon illustrations by Andrew Slocombe add delightful dimension of humor. They would be a wonderful source of inspiration for T-shirt designers. The book is a companion volume to Statistically Speaking (see ARBA 98, entry 82) and Physically Speaking (see entry 000), both collections of quotations related to fields of science. Mathematically Speaking will have infinite appeal for the wider public interested in mathematics.

Marilynn Green Hopman

Mathematics Teacher Volume 92, Number 7, October 1999

With the well-thought-out organization of this collection, teachers and students can easily identify the author or source of a mathematically related quotation. They can also verify the wording of a quotation or find quotations on a specific topic. The content, which varies from intensely thought provoking to rib tickling, includes such items as philosophical classics, song lyrics, and poems.

The large number of citations also exposes readers to wonderful publications with which they might not otherwise become familiar. Within the 120 highlighted topics, the reader will occasionally question the necessity for including particular quotations and will suppose that the authors chose to err on the side of inclusion rather tan exclusion. A few of the quotations contain questionable language and sexual innuendoes that might offend some students and parents, but these quoutations could easily be avoided. The typical teacher will find frequent use for this excellent resource.

Jeanne Ramirez Corpus MatherUniversity of Science and Arts of Oklahoma

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