This is an interesting and varied collection of writings about mathematics, most published in journals in 2010. It is marketed as “popular mathematics” but the articles are much more scholarly than what is usually placed in this category. As an indication of the level we are talking about, consider that of the 26 articles, four appeared first in Notices of the AMS, two in Mathematical Intelligencer, and one each in College Mathematics Journal and American Mathematical Monthly. This is the second annual installment of the series (the first issue is reviewed here ).
The coverage is slanted heavily toward applications of mathematics, although there are healthy slugs of math education and philosophy of mathematics too, as well as a few hard-to-classify essays. The articles are very much “about” mathematics and not “of” mathematics — they show little or no actual mathematics, but do show how mathematics is used (and misused), what its practitioners are like, and some of its societal impacts.
Here are some of my favorite articles from the book. Pictures are always good, and there are two lavishly-illustrated articles on mathematically-based sculpture: James Hamlin & Carlo Séquin’s “Computer Generation of Ribbed Sculptures” and Helaman Ferguson & Claire Ferguson’s “Celebrating Mathematics in Stone and Bronze”. Another article with lots of drawings is Ivan M. Havel’s “Seeing Numbers”, a look both at how numbers are visualized and how visualization may be used in unusual ways to solve problems. It includes a long discussion of mathematical savants who can recite thousands of digits of pi or somehow sense whether a number is prime or not, with some speculation on how they might accomplish these tasks.
A couple of articles deal with policy issues. David J. Hand’s “Did Over-Reliance on Mathematical Models for Risk Assessment Create the Financial Crisis?” is not mathematical at all, but deals with the general problem of how business leaders can make decisions based on recommendations from technical experts when the leaders don’t understand the basis of the recommendations. Underwood Dudley’s “What is Mathematics For?” makes a convincing argument that most people don’t need to know any mathematics past arithmetic. (Unfortunately it follows this with an unconvincing and antique argument that everyone should study math anyway, for its mental-discipline benefits.)
One article that actually has some significant mathematics is Erica Klarreich’s “Playing with Matches”. The National Resident Matching Program matches medical students (and, increasingly, medical-student couples) to hospital residency programs. This is a variant of the stable marriage problem, but the requirement to accommodate couples makes it more complicated and the existence of a stable arrangement is no longer guaranteed.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.