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Number Story: From Counting to Cryptography

Peter M. Higgins
Copernicus Books
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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When reading a new book about numbers such as Number Story, I am inclined to go into the experience looking for an answer to this question: How is this book different from the collection of similar books currently on my shelves? That collection includes The Penguin Dictionary of Curious and Interesting Numbers, The Book of Numbers, The Universal History of Numbers, and The Kingdom of Infinite Number, to list the titles I can see by spinning around in my desk chair. I am by no means averse to reading again about the Fibonacci numbers or the complex plane, but I am more attracted to the possibility of finding something new in old territory.

Number Story meets that challenge very well. In the book’s discussion of divisibility tests, one can find tests for determining whether a number is divisible by any integer from 2 to 16. This includes, to the author’s credit, the challenging tests for divisibility by 7 and 13. I went into chapter 3, which covers these tests, specifically looking for the “divisible by 7" test, the presence or absence of which is one of my main criteria for evaluating textbooks for my Mathematics for Elementary Teachers course. (My rationale there is that grade-school kids will ask about that, and a future teacher should be prepared with an answer.) The fact that the test is there, along with the bonus test for divisibility by 13, which is far less commonly seen, speaks well of this book.

Also present, and part of the “something different” list, is a fairly straightforward explanation of the Monster group. This appears in the context of discussing its size as an example of a large number whose status will never be co-opted by a future discovery (a fate which ever awaits the largest-known prime number).

Additional novelty in this book is present with the final chapter, “For Connoisseurs”, which includes more mathematically rigorous illuminations of many of the book’s material (including, of course, the divisibility tests above — but not the Monster). This serves nicely to cap off a worthy addition to popular books on numbers.

Mark Bollman ( is an associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

Preface; The First Numbers; Discovering Numbers; Some Number Tricks; Some Tricky Numbers; Some Useful Numbers; On the Trail of New Numbers; Glimpses of Infinity; Applications of Number: Chance; The Complex History of the Imaginary; From Imaginary to Complex; The Number Line Under the Miscroscope; Applications of Number: Codes and Public Key Cryptography; For Connoisseurs; Further Reading.- Index