The Secret Life of Numbers: 50 Easy Pieces on How Mathematicians Work and Think

We should persuade the New York Times to translate and syndicate George Szpiro’s columns from the Swiss newspaper Neue Zürcher Zeitung (NZZ) and its Sunday edition NZZ am Sonntag. That way we would not have to wait years to read his musings. He writes about mathematics for the general reader, and he has a knack for that, for giving readers “…an understanding not only of the importance, but also of the beauty and the elegance of the subject.” In The Secret Life of Numbers, the subjects include solved and unsolved problems, mathematical personalities, historical tidbits, and a potpourri of applications.

Szpiro’s background is worth a brief mention. His primary occupation is journalism, though he has done graduate work in mathematics, has an MBA from Stanford and a PhD in finance and mathematical economics from Hebrew University . Consequently, he is a specialist in virtually none of the areas he writes about and this is a great advantage. As a journalistic polymath of sorts, he conveys general concepts very clearly with well-chosen details.

Since most of the pieces in Szpiro’s book are only three or four pages long, he faces the challenge of communicating something meaningful about complex concepts to a general reader in an entertaining way, and doing so in at most a few thousand words. Generally he does so very well. For example, he discusses the Poincaré conjecture and Perelman’s work in three and a half pages and manages to tell the history, describe the problem in a comprehensible fashion and give a general idea of the proposed solution.

There were several pieces that I particularly enjoyed. There is a sly portrait called “God’s Gift to Science” about Stephen Wolfram and A New Kind of Science. (The title of the piece speaks for itself.) There are three articles about Thomas Hales’ work on the Kepler conjecture and honeycomb problem. A selection on the computer scientist Danny Hillis talks about his career as an “Imagineer” for Disney, his work on a 10,000 year clock, and his new company called Applied Minds. I also enjoyed a piece on a Swedish student’s purported solution of Hilbert’s 16^th problem.

Generally, the applied pieces in the book’s last section don’t work quite as well as the other articles. There is, however, a good account of Lawrence Sirovich’s information-theoretic analysis of Supreme Court verdicts.

This is an excellent book to dip into, to give to friends or relatives who wonder what you do, or to recommend to students.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.