Tuesday, February 25, 2014

e The Story of a number Review

e The Story of a Number, by Eli Maor, is a fascinating book in which Maor does an outstanding job of explaining the origins of the number e even though the origins of e are not very clear. There are many great mathematicians that have in some way contributed to the discovery of e For instance, John Napier dedicated 20 years of his life to create continuous logarithmic tables (by his definition of logarithm). He didn’t discover the number e, but he came surprisingly close, and his work in the development and understanding of logarithms were vital in e's discovery. 
In Eli Maor's promulgation of the origins of the number e, he provides the reader with an evolutionary perspective of mathematics by presenting the history of these great mathematicians, their contributions and discoveries that have developed mathematics, and the mathematical proofs and equations themselves. It's the fine job that Eli Maor does of balancing these things that allows for a better understanding of the different contributions vital to the evolution of mathematics and the discovery of e. For example, in the 1600's both Newton and Leibniz discovered calculus, and the only differences between their techniques were the forms of words and symbols of which they used.  They did not discover the number e, but without their contribution to the developments of calculus we would not have known how to differentiate. AND furthermore, we would not be able to declare the function  y=e^x as the function that equals its own derivative.
Eli Maor goes beyond the discovery of this mystical limit/number thing, e, by discussing how great mathematicians such as the Bernoullis’ and Euler have further expanded the far reaching capabilities of mathematics by combining calculus, trigonometry, and mathematical analyses using e, pi, and i. Not only will the reader gain a better understanding of the origins and evolution of different mathematical techniques and notation that are used today, the reader will gain a better understanding of the beauty of mathematics in its ability to explain the natural world we live in.
There are some chapters of the book that at first seem out of place, or irrelevant to the previous chapter or page, but Eli Maor is purposeful in choosing when to introduce certain topics, as well as when to delve into certain topics so that the reader is better prepared for topics later on. Overall, this book is a great read for those with a moderate level of mathematical knowledge, and will definitely provide insight as to the origins of one of the greatest, perhaps most mystical, numbers of all time, e.