In *Numerology or, What Pythagoras Wrought* Underwood Dudley examines and exposes the fallacies of a wide spectrum of number misconceptions. A root of many inappropriate uses of numbers lies in the Pythagorean notion that "all is number," a notion which attributes to numbers emotional or physical properties which they do not possess. From this source the magical misuse of numbers has spread to an almost unbelievable extent.

Two of Dudley's purposes in this book are

- to expose the misuse of numbers by those who use numbers as though they contained magical influence; and
- to counter those who ascribe numerical values to various other entities and then see special numbers appearing with what seems to be inexplicable frequency.

He achieves these goals, while also engaging the reader with a thoughtful yet entertaining style.

*Numerology*, as hinted above, deals with more than just number magic. Various gematria procedures (assignments of numerical values to letters to allow words to correspond to numbers) are presented, explaining how, for example, many historical figures have been given the number 666 (the number of the beast, in Revelation 13:18).

A comparatively small part of the book deals with numerology itself, that is, the derivation of digits from one's names, birth date, etc. and interpreting the digits according to (somewhat) standard rules to read one's personality and fortune. These techniques can be used to decide on a suitable place to live or the proper times and dates for important activities. One can also use numerology as a guide in one's relationships with other people.

The fascination of some with numbers derived from measurements of Stonehenge and/or the great pyramid of Egypt is another Dudley target, as are biorhythms and the erroneous discovery of the golden ratio in strange places. Less familiar topics in this book include rithmomachy (a game played in Europe between about 1000 and 1600 and involving a sense of strategy coupled with skill in addition), number forms (mental diagrams some people have for numbers), and Elliot Wave Theory (a tool for stock market analysis).

Since many of the topics Dudley covers are themselves the subjects of whole books (Dudley gives references), Dudley's descriptions are necessarily incomplete. He does not, for example describe all the ways numerologists get digits from names. He does, however, present a wealth of information on topics he chooses, and ably argues against those who make erroneous conclusions based on the numbers they find.

One of Dudley's tenets appears on page 286: "The question is, should mystics and mathematicians try to communicate with each other? *Can* they communicate? I think that their worlds are too far apart." If you don't share that belief, his (tongue-in-cheek) warning on page 72 might merit your attention: "The numerological implication of 1998 is clear: 1998 = 666 + 666 + 666. We should, I think, be very careful in 1998."

I found both pleasure and new insights from reading Dudley's *Numerology*, and I think many professionals in mathematics -- and their students -- would share these feelings.

Walter Sizer is a professor of mathematics at Moorhead State University, currently on sabbatical and visiting at URI. Mathematical interests include abstract linear algebra and the history of mathematics; hobbies are bird watching and travel.