### 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you might expect throughout the rest of the book with a mix of historical
references, humorous or fascinating stories, and descriptions of the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.

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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