Princeton, NJ: Princeton University Press, 1994. 284 pages. $24.95
Numbers are our friends. It may not be too far fetched to think that numbers can hold as much interest as words. Many numbers have known origins and some--notably four of the five fundamental constants in mathematics: !, i, 1, and 0--have very interesting tales associated with them. But the number e, the fifth fundamental constant and the base of natural logarithms (as opposed to common logarithms with base 10), has its own story. In e: The Story of a Number, Eli Maor tells this story as if opening a Chinese box, with each account opening the way to another and then another, each within a box that offers yet another surprise.
The way money grows with time, the area under the hyperbola y = 1/x, the limit of (1 + 1/n) sup n as n approaches infinity, the "natural" base of logarithms, and that function e sup x equal to its own derivative, are all definitions or applications of e. But the story of e, as told by Maor, is much more than remarkable relationships among numbers and symbols. This is a story of discovery with side trips into the lives of famous and not-so-famous men (only one woman, and this in an imaginary conversation between Johann Sebastian Bach and Johann Bernoulli, is mentioned in 191 pages of text) and their ways of thinking, and of connections between and among numbers, people, and ideas.
Although the dust cover states that the book is "(g)eared to the reader with only a modest background in mathematics," readers without some preparation in calculus may have difficulty following Maor, particularly when he uses first-and second-order differential equations to illustrate the development of exponential functions. Readers will not suffer formula deprivation. A willingness to appreciate the words, to accept the formulas, and to be content to skip a few paragraphs will reward even those readers with less than modest backgrounds in mathematics.
Maor includes examples to show that mathematicians demonstrated their facility with language by preparing manuscript and book titles such as "Meditation upon Experiments made recently on the firing of Cannon," (Euler); "Description of the wonderful canon of logarithms," (Napier); and "New solid geometry of wine barrels," (Kepler). Those interested in American history may find a footnote Maor cited intriguing: "...the first nine digits of e after the decimal point can be remembered by e = 2.7(Andrew Jackson) sup 2 , or e = 2.718281828...because Andrew Jackson was elected President of the United States in 1828. For those good in mathematics, on the other hand, this is a good way to remember their American history."
And why was e chosen as the letter? …