Review of

**Mathematics
Without Apologies: Portrait of a Problematic Vocation**,
by Michael Harris, Princeton University Press, Princeton, New Jersey, 2015. 464
pp., $29.95 (hardbound). ISBN 9780691154237.

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The
title is obviously a reference to the classic book by G. H. Hardy, “A
Mathematician's Apology” and Harris acknowledges that fact. Hardy’s book is one
that all math students should read, for it contains a great deal of wisdom
regarding what mathematicians do and how they fade over time.

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This book goes far deeper into what
mathematics is and what it is that mathematicians do. There is a lot of
philosophy, an occasional splash of silliness, a great deal of the history of
mathematics and many mentions of some of the quirks of famous mathematicians. Harris
also throws in many autobiographical references.

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The mathematics itself is all over the
spectrum, from extremely abstract and complex ideas to simple concepts such as
a small complete graph. One person that is repeatedly mentioned is Alexander Grothendieck, an incredibly prolific
mathematician that was also higher on the scale of eccentricity than most math
people.

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Although there is the occasional mention of
very advanced mathematics, this book is generally a work of popular mathematics
and nearly all can be understood by nearly all. Even though it is
understandable, it is sometimes a slog to read through it as it occasionally
descends to the level of tedium. If I were to assign this as a reading in a
math class it would examined one chapter at a time. That is due to the major
problem of the book, the lack of continuity.

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This book was made available for free for
review purposes

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