e: The Story of a Number

But e remains, the center of the natural logarithmic function and of calculus. Eli Maor's book is the only more or less popular account of the history of this universal constant. Maor gives human faces to fundamental mathematics, as in his fantasia of a meeting between Johann Bernoulli and J.S. Bach. e: The Story of a Number would be an excellent choice for a high school or college student of trigonometry or calculus. --Mary Ellen Curtin

Product Description

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest background in mathematics, this biography of e brings out that number's central importance in mathematics and illuminates a golden era in the age of science.

This book will give you a great understanding of what calculus is all about.


A very interesting book about a curious number...   June 5, 2000
Stephen Armstrong (Hadley, Ma USA)
12 out of 12 found this review helpful

Galileo wrote that philosophy is written in the grand book of the universe, in a language of characters, circles, triangles, and other figures. Somewhere in this grand offering came the number e, which is the limit of the expression (1+1/n)^n, as n approaches infinity. It is a curiosity number, one that bridges Napier's original logarithms (which are to the base 1/e) and the origins of calculus. It was discovered at a time of exploding international trade, which is based on compound interest, whose formula you will recognize in the definition of e. It is the base of natural logarithms, a non-terminating, non-repeating decimal. e cannot be the solution to a quadratic equation that has integer coefficients.

This is a splendid book about a number as strange and useful as pi. Well written, this book can be handled by bright high school students and college students who have an interest not in solving math problems (the way we usually teach math), but in the history of math and this curious number. I read it for general interest and was very pleased with the entire book.


More than the story of the second-most famous number   November 9, 2004
Duwayne Anderson (Saint Helens, Oregon)
20 out of 22 found this review helpful

This is the second book by Eli Maor that I have read and reviewed in as many months (the previous book was "To Infinity and beyond"). As I was reading this latest book I thought several times that the title was wrong. I think a more appropriate title might be "A popular introduction to calculus" or "The road to calculus." Then, again, he does more than just calculus, too. So I'm not sure what to call it. It's more than just about e, and it's more than just about calculus. It's all that, with a lot of other interesting tidbits tied in as well. While Eli does spend quite a bit of time discussing e, this book goes well beyond a simple linear history of a number that's fundamental to modern mathematics.
Eli begins his story with John Napier and the invention/use of logarithms as tools for calculation. I found this introduction interesting because it reminded me how valuable calculation tools were, in the days before electronic calculators. I even found myself rummaging through my desk for that long-forgotten slide rule and remembering with a degree of nostalgia the many hours spent working through problems in mathematics and physics during my high school years, and how I'd pride myself on being able to carry the a full three significant digits through a complex sting of calculations.
It seems as though the initial chapters of Maor's book deal more with the history of e than does the middle of the book. Somewhere around page 40 Maor moves away from mathematical history aimed squarely at natural logarithms and focuses more on what is (I suspect) his true love: calculus. This is one of the best introductions to calculus I've seen, primarily because Maor did such a nice job of bring together all the historical footnotes.
Coincidentally, as I was reading Mayor's book my wife was taking a class for teachers, aimed at educators who teach calculus in the middle and high schools. She found the book immensely helpful in both dealing with the actual mathematics in her class as well as providing insight into ways of introducing concepts relating to higher-level mathematics to young students. She introduced Mayor's book to other students in her class, as well as the professor (who had read it already, of course), all of whom enjoyed it immensely.
In terms of the history that he covers, I thought the discussion relating to Newton and Leibniz was the most interesting. My own coursework in Physics used Newton's dot notation, while my courses in mathematics adopted Leibniz's differential notation. Reading Maor's book provided a bit more insight into the historical quirks that led to the notation in common use today.
Especially interesting was his discussion about Newton's approach to the calculus. I think that if students had to use the notation and approach first used by Newton, calculus might still be relegated largely to the college curriculum. I really had no idea, before reading Maor's book, how convoluted Newton's approach was in comparison to that used by Leibniz. Newton is often portrayed (rightfully so) as a genius, and Mayor's description of Newton's calculus left me marveling that Newton managed to work through it as he did, given the (relatively) more difficult approach he took.
The end of Maor's book uses the calculus to illustrate several examples showing how e appears in various mathematical and physical problems. There are examples using aerodynamic drag, music, spirals, hanging chains and the cycloid. No discussion of e would be complete without a nice explanation of the function that is its own derivative, which Maor tells with characteristic clarity.
Frequently while reading Maor's book I found myself wishing I'd had this introduction before taking several of the classes I took during my school years. His treatment of the complex plane, for example, is as clear as his introduction to basic ideas in calculus. Looking back on my first class in complex variables, I recall the fog that surrounded my initial introduction to conformal mapping. Maor, though, makes it easy. With the skill of a master educator, he manages to explain the concept with such ease that you learn the essential ideas almost before you realize where he is taking you. Though most texts of this sort would not tread on a subject as foreboding to the general public as the Cauchy-Riemann equations, Maor explains the basic concepts as clearly and almost as effortlessly as he does conformal mapping. Ordinarily I wouldn't think it's possible to explain Cauchy-Riemann in a book that's intended for the general public with an interest in mathematics, but that's what Maor does, and he does it well.
In short, this nice little book manages to cover a lot of mathematical territory with the skill that only a master educator can muster. It is definitely a whole lot more than just the story of the second-most famous number in mathematics.


Compelling and easy to read   June 11, 2006
Luis Mansilla Miranda (Vina del Mar, Chile)
8 out of 8 found this review helpful

I know calculus but I didn't know much about some of the history of mathematics. How easy is to learn a complex theme in the words of this author. A fascinating book about an important number, browsing the history of logarithms, then some of the history of calculus and finally the history of Leonhard Euler, and the first appearance of "e". Obviously you find mathematics in this book, but presented in a easy-to-understand way.


Good Balance of Math and History   December 24, 2005
Ronald Brown (Florham Park, NJ USA)
6 out of 7 found this review helpful

For me, this book had the exact right balance of math and history. There is some mathematical discussion but nothing to scare anyone who has taken calculus. The historical discussion really helps one understand how mathematical thought has evolved over the last few hundred years.