e The Story of a Number Book Review

The book e The Story of a Number by Eli Maor is about the history of many mathematical concepts, including the number e.  Maor introduces each of the concepts he discusses through first describing the works and personality of the famous mathematicians who discovered or invented each of the concepts and then showing how the mathematicians came up with their discoveries.  He relies heavily upon anecdotes about the mathematicians to keep the reader who isn't already absorbed in the math engaged with the text.  Overall Maor's purpose seems to be to show that although e's history isn't widely known, it is related to or rooted in many other topics, some of which have much more extensive histories.

If a reader didn't look at the title, he might not know the book is about e until he was over half through it.  This is most likely due to the fact that there isn't a lot of historical material on e as there is, for example, with π.  So Maor begins with the concepts leading up to e, starting with logarithms and their inventor John Napier for the first two chapters.  In doing so, he presents a precedence for what you might expect throughout the rest of the book with a mix of historical references, humorous or fascinating stories, and descriptions of the math.  This mix works quite well together, with each portion balancing the others out.

Following the first two chapters, Maor inserts one of many small inter-chapter sections.  In the first one, he describes and gives examples of computations done with log and anti-log tables, directly relating to the beginning chapters.  Many of the other sections are closely related to the chapters as well, but a few are loosely related.  Their topics range from numbers related to e to indivisibles to parachuting.  The most memorable one was certainly a fictitious conversation created between J. S. Bach and Johann Bernoulli, who as Maor notes, most likely never met.  The conversation was mildly awkward and filled with talk relating math and music (of course).  It was just believable enough to have been an actual written record of a meeting.  These sections offered a nice change of pace and presented a good outlet for Maor to interject interesting ideas that didn't fit exactly into the normal flow.

The third and fourth chapters drop the topic of logs and switch to finance and limits.  Maor goes further back in time for a moment to describe money and interest, but most of the book describes parts of the last 500 or so years of mathematics.  Maor's first significant mention of e occurs in these two chapters in relation to the limit of a function for annual interest rate.  Maor moves from limits to the ideas leading up to calculus in chapters five and six.  He talks about the Greeks and their difficulties with calculus, before returning to more recent history.  Maor goes into depth on more ideas that led to calculus before moving on to the topic of the area of a hyperbola.  The math being described starts to be at a higher level at this point than previous parts of the book but is well explained.  These chapters moved at a good pace and didn't present any difficulties with challenging ideas, while still presenting quality information.

Maor then has a lot to say about calculus and Isaac Newton and Gottfried Wilhelm Leibniz in the following couple of chapters.  Maor provides background info and more nice anecdotes that give life to the mathematics he describes that follow the history.  He touches on the feud between Newton and Leibniz and the effects that follow.  Some of the anecdotes throughout this portion of the book give the reader a great idea of what the mathematical climate really was like at this point in time.

After the calculus portion, Maor gets serious about e, going into depth about 𝑒ˣ.  Maor continues on in the next chapter with information on the Bernoulli family and how their discoveries relate to e and polar coordinates and the logarithmic spiral.  The twelfth chapter is on the Hanging Chain problem and if its solution is related to e.  Maor then talks about Euler and the crazy things he did with e before moving on to imaginary numbers and their relation to e.  These chapters give e and the concepts surrounding it some real color, allowing for easy interpretation and understanding of sometimes obscure topics.

The conclusion describes what kind of number e really is, which is an excellent ending to an information packed book.  This book is for the math lover first, the number lover second, and the history lover third, but all would thoroughly enjoy this book, although likely for different reasons.   


Comments

  1. Good review. I think people will be able to tell directly whether they would like to read, plus some useful info even if they don't.

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