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A Century of Mathematics: Through the Eyes of the Monthly (Spectrum)

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A common phrase used to describe the experience and qualifications of undergraduates is "mathematical maturity." Well, that phrase can be used to describe the theme of this collection of items from The American Mathematical Monthly. For mathematics has indeed matured in the United States in the last century and this work provides a series of documentary snapshots. A veritable army, this reviewer included, unites in criticizing the current poor state of mathematics education in the United States.
However, we forget that the United States was a mathematical backwater until large numbers of mathematicians immigrated from Europe in the interwar period. Also, first-year students are now routinely taught material that would have been beyond that of many instructors at the turn of the century. There was a strong movement by colleges to eliminate mathematics requirements in the 1920' s. And the extensive growth in the numbers of mathematics students was largely a direct consequence of World War II.
The obvious military benefits of technological superiority, largely imported from Europe to win the war, had a mathematical base. Furthermore, the GI Bill of Rights provided the money for thousands to attend college. And the growing conflict with the communist block helped fuel the technological fires, with extensive federal dollars made available for research. In mathematics, this led to a schism into the pure and applied factions that still exists today, although the continuous connections are more apparent than many will admit.
The editor does a good job in selecting pieces that reflect all of this, providing a good deal of evidence indicating that this is indeed the best of times. Like all other human endeavors, mathematics mimics the society that surrounds it, and many social movements are reflected in the material.
Like pi and e, some things stay constant. Instructors always question current teaching practices and complain about the poor quality of students. This is not a bad thing, for as long as these complaints are with us, mathematics will continue to thrive and advance.
If you have any interest in how things have developed over the last one hundred years, pick up this book. Like members of a family, mathematicians have a heritage and roots to their ancestors, and it does us all good to honor them from time to time.

Published in Journal of Recreational Mathematics, reprinted with permission.