Sunday, January 31, 2016

Review of "Mathematics Without Apologies" by Michael Harris

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.

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.

 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 people.

 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 review purposes

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