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Mathematics and Its History: A Concise Edition

John Stillwell
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Michele Intermont
, on
This is a beautiful book. It will not be new to some readers, as it could/should be considered a 4th edition of Mathematics and Its History.  The third edition was reviewed here
The first edition of the book weighed in at about 350 pages.  By the third edition, there were 650 pages.  The Concise Edition returns to 350 pages, with several substantive changes.  The author claims that a motivating factor for the new edition was to have a book that would feel like a book for a one-semester course.  This does; it would be fun to teach a course from it and I hope to get that chance.   
What’s missing beyond 300 pages?  Really, nothing.  This book flows so well that I did not feel anything was lacking from it.  But more concretely, the first 5 chapters are almost exactly the same as in the first edition (and in the 3rd, with renumbering); the chapter on Number Theory in Asia from the 3rd edition is gone. The chapters on mechanics, simple groups, hypercomplex numbers, and combinatorics have been removed (of these, only Mechanics also appeared in the 1st edition).  Most of the chapter on differential geometry has been deleted. The chapter on Topology has been pared down.  The chapter on algebraic number theory from the 3rd edition has been pared down and rearranged as part of a chapter on commutative algebra. Some other topics have been moved around too.
In addition to the changes to the content as noted above, the biographical notes that ended each chapter have been removed.  Some readers will lament this, I am sure, but as the author points out, there are several places on the web to attain short biographies of mathematicians. 
And the Concise Edition (as well as the 3rd edition, I believe, but not the first edition) contains wonderful one-page summaries to begin each chapter which provide context as well as make connections to other chapters.  
I am confident that the many readers of Stillwell’s work will find it satisfying and worthwhile to update their libraries with this edition. Those currently unfamiliar with his work will find this a delightful place to begin.
Michele Intermont is an Associate Professor of Mathematics at Kalamazoo College. Her interests are in algebraic topology.