e: The Story of a Number

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.

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 Le

A definitely recommended read, pure mathematical beauty - this book shows how the mathematicians worked - it shows how Napier evolved the logarithms, how leibnitz and newton approached calculus, and how the number e itself was discovered... its so simple to read, and it also shows exactly how the firsts proved their theorems... unlike textbooks we have read proofs in. And a very quick and simple read too - where one is exposed to the beauty of mathematics when one sees how 'Pi' came to have its myriad infinite series expansions..A chapter here is devoted to the Bernoulli family - which is where I want to draw your attention. This is perhaps the most influential family in mathematics, where three generations of the family have made staggering contributions to physics, mathematics, astronomy, finance, etc etc. And the family is as insane as can be - The brothers Jacob and Johann were the first to sit and understand Leibnitz' calculus, and Johann was a staunch supporter in the fued with Newton, on Leibnitz' side...(btw - Newton destroyed Leibnitz professionally, after Leibnitz' death... and Leibnitz funeral was attended by his secretary only... none else). So soon Jacob and Johann fight like mad about who made certain proofs - and Johann leaves the house, promising to return only after Jacob's death. Which he does. Later Johann and his son, who were working together starting arguing on who's name should come first on the documents they published,... so they soon quarelled and began to work alone... and then later, when Daniel starting publishing more than his illustrious father, Johann expelled him from the house with a warning to never return...In the above book, Eli Maor also compares the Bernoulli achievements in maths, with the other family that had a 150 years of three generations of contributions to its field - which was also a contemporary - viz. the Bach's and music. Awesome book - clean and nice, and leaves you admiring the poetry of maths... The book closes on the marvellous work of Euler who shows 'e power i, pi = -1', and thus links the three most vexatious numbers in maths, e, pi and i (sqrt -1), in a most wonderfully simple equation. What sheer elegance, and what beauty indeed.

To those of you who are not familiar with Maor, let me point out that he is a mathematician (as opposed to a lot of the other people who write popular math books) with an immense knowledge of math history and also an excellent writer. Some reviewers have compared this book to books like "An Imaginary Tale" by Paul J. Nahin and "History of Pi" by Petr Beckmann. This is totally missing the point. Both of those books are written by non-mathematicians, and contain error that will annoy mathematicians. Maor on the other hand is a superb scholar. I've read all his four books quite carefull, and I've not found any errors.This book will give you a great understanding of what calculus is all about.

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.