In A Cultural Paradox, we have a small — both thin and pocket-sized — volume containing 57 short chapters, each a brief recreational essay on a mathematical topic. The author’s declared goal in pulling these nuggets together is to dispel the apparent paradox in the title and to show the reader that mathematics can indeed be fun.
While this is an admirable goal, the book falls far short of its aims. It may be that, for example, it’s not possible to distill non-Euclidean geometry to a page and a half and not have it feel very rushed and superficial. If so, it’s just not a good idea to try to do it. A chapter entitled “Economic implications of Gaussian Copula Functions” mentions the function without defining it or even indicating what makes it important. An attempt to describe the E8 algebra and its connections to physics probably shouldn’t have been attempted in one page.
There are occasional chapters that show promise, such as “When Nothing Is Something”, on the importance of the number zero, but they are few in number. Several chapters could serve as the opening for longer works, but reading them alone, one is left feeling out of breath and unsatisfied. By the time I reached the final chapter, which explained the significance of “QED” and claimed that it stands for “quod erat faciendum”, I was almost too worn out from counting errors to note that there should be a really good explanation when an author publishes something this apparently contradictory.
Mark Bollman (firstname.lastname@example.org) is associate professor of mathematics and chair of the department of mathematics and computer science at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.