Review of "Mathematics Without Apologies" by Michael Harris
Without Apologies: Portrait of a Problematic Vocation,
by Michael Harris, Princeton University Press, Princeton, New Jersey, 2015. 464
pp., $29.95 (hardbound). ISBN 9780691154237.
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.
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.
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
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.
This book was made available for free for