Mathematical Evolutions (Spectrum Series)

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Summary: How many of the main math ideas developed
Review: Advances in mathematics are no different from those in other fields. A new result is generally the consequence of years, sometimes centuries of effort, by many people. Revolutionary results are rare, with evolutionary being a far more accurate descriptor of the movement of mathematical progress. Although mathematical progress happens faster than evolutionary changes in organisms, there are many parallels.
When a new environment becomes available, many different creatures move to occupy it and within a very short time, new species have branched off and are flourishing. Upon the development of a new area of mathematics, many branches rapidly rise and shoot off in many unexpected directions. Different creatures in isolated environments evolve to fill a common ecological niche and possess almost identical characteristics. Different mathematicians often work on the same problem independently and arrive at similar breakthroughs at roughly the same time.
With all of these similarities, it is only natural that mathematical topics be examined from an evolutionary perspective. In 1993, John Ewing, then editor of the "American Mathematical Monthly" approached one of the editors of this book (Abe Shentizer) with the idea to start a regular column "The Evolution Of . . . ", which was to chronicle the development of a mathematical idea. The columns were to be accessible to a general, albeit knowledgeable mathematical audience. This book is a collection of those columns.
The historical development of some of the basic concepts such as function, integration, optimization, rings and elliptical curves are described in great detail. While formulas are used, they appear only when necessary, which is fairly rare. This is a tribute to the quality of the exposition, which generally renders any use of equations redundant. The authors also are to be commended for their spending the time to explain the historical context of the discovery as well as some of the consequences.
Properly done, essays in the history of mathematics explain where the idea was first described, the background that led the discoverer to the discovery, the personal and professional interactions of the discoverers and where the discovery fits in that fascinating, interrelated jigsaw puzzle called mathematics. The essays in this book are properly done.

Published in the recreational mathematics newsletter, reprinted with permission.