Reviews of Letters to a Young Mathematician
by Ian Stewart

(Perseus, $22.95, 224 pages, April 2006)


The Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work and Think
by George G Szpiro

(Joseph Henry Press, $24.95, 210 pages, March 2006)

Two Science Shelf Guest Reviews by Julie Falkner, published with permission of the author

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Have you ever paused to ponder the mathematics of rainbows? Or why -3 * -5 gives +15? ("Just because" is not an adequate answer!) Perhaps you've wondered what research mathematicians actually do? All these topics and many more are covered in this series of twenty-one letters from an established mathematician to his niece, "Meg." Initially, Meg is a high-school student who is curious about career prospects for mathematics graduates, but as the letters progress she develops into a Ph.D. candidate and finally becomes a tenured academic.

The avuncular letter-writer of Letters to a Young Mathematician is Ian Stewart, a mathematics professor at the University of Warwick in England and author of numerous popular mathematics books. He has a rare gift for removing unnecessary layers of complexity to make an often obscure subject accessible to a general reader. For example, in his letter about "Fear of Proofs" he uses a children's word puzzle to explain the concept of mathematical proof. His brilliant exposition is a model of clarity and perfectly illustrates his point about the need for rigor.

Other letters cover topics ranging from the fundamental--the importance of reading around one's subject--to the more esoteric, such as how to optimally wrap tennis balls in six dimensions, and whether a recently proposed proof of the Poincare conjecture is indeed correct. Somehow Stewart always knows when to provide details and when to withhold them, so that his reader never becomes bogged down.

Some of the most interesting letters are also more personal. In "How I Almost Became a Lawyer," Stewart discusses the factors that led him to become a professional mathematician. Later he gives an account of the process of discovering a specific proof, an intriguing story that features doodling on the Warsaw-Krakow train.

Letters to a Young Mathematician is essential reading for all those who are somewhere on the path from high-school fascination with mathematics to Ph.D. student. And it is also highly recommended for the mathematically curious amateur, who will capture some of Stewart's enthusiasm for the beauty and importance of his field.

Julie Falkner is a New Zealander now living in Canada. Her wide-ranging career has included teaching University mathematics, developing mathematical software, and freelance writing. She loves to read, to travel, and to explore history.

Science Shelf owner Fred Bortz has written a similar book for younger readers, To the Young Scientist.

Mathematicians have beautiful minds. But except for one or two movies and the occasional headline about an unexpected new proof, their subject generally has a low profile. So it's a treat to come across a book such as The Secret Life of Numbers that reveals the amazing diversity of mathematics without getting too technical.

The book starts with the problem of correcting our calendar--how often do we need leap days, given that the true length of the year is 365.242199 days?--and ends with the statistical search for codes in the biblical book of Genesis. Other pieces deal with huge prime numbers and their connection to credit card security, and how roundoff errors can cause a rocket to explode. And the politically minded will enjoy reading about the Alabama paradox.

Author George G. Szpiro is a trained mathematician who is now a journalist, and these 50 Easy Pieces on how Mathematicians Work and Think were originally published as a series of columns in a Swiss newspaper. As a result there is an element of repetition, and it becomes annoying. For example, when you meet Thomas Hale for the fourth time, you're no longer interested in honeycombs. Moreover, the word "easy" in the subtitle begs the question, easy for whom? Realistically, the more theoretical pieces will be "easy" only for those who have studied some University-level math.

But anyone can appreciate Szpiro's section of mini-biographies, covering both historical figures and mathematicians still working today. He's sometimes refreshingly frank when assessing their contributions or commenting on a premature press release.

If you're attracted by the wide applicability of mathematics, keen to learn about new ways to generate random numbers, or merely curious about beautiful minds, you'll be intrigued and edified by The Secret Life of Numbers.

Julie Falkner is a New Zealander now living in Canada. Her wide-ranging career has included teaching University mathematics, developing mathematical software, and freelance writing. She loves to read, to travel, and to explore history.

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