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Undiluted Hocus-Pocus Reviewed by Andy Magid Book Review Undiluted Hocus-Pocus Reviewed by Andy Magid Undiluted Hocus-Pocus: The Autobiography of coming one of two Martin Gardner possible answers to Martin Gardner the trivia question, Princeton University Press, 2013 who is the most im- US$24.95, 288 pages portant nonfiction ISBN-13: 978-0691159911 writer from Tulsa? The other possible At one time, algebraists used to entertain them- answer is the histo- selves with the pseudotrivia question: who is rian Daniel Boorstin, the most important ring theorist from Alabama? who was also born “Pseudo” because the point was not to test the in 1914 but arrived interrogee’s knowledge of Cotton State mathemat- in Tulsa as an in- ics, but to surprise them with the answer, namely, fant. Both men grad- Nathan Jacobson. That it should be a surprise uated from Tulsa carried more than a whiff of Yankee chauvinism; Central High School, anyone familiar with the Midwestern U.S. small although Boorstin, town merchants of the 1940s and 1950s who were something of a prodigy, seems to have graduated born in Poland and raised in the American South at age fifteen before Gardner entered. I do not would have instantly recognized from Professor know if they ever met. Incidentally, even though I Jacobson’s speech patterns that he shared that met these men only briefly and then near the end biography. And the algebra community being the of their lives, I spoke to them enough to know size it is, anyone who could have been surprised by that you couldn’t detect anything in their speech the answer was surprised long ago, although there patterns suggesting a Tulsa biography, not even in is a similar question still making the rounds—who the telltale second person plural. is the best group theorist from Arkansas?—that There’s also the academic historian John Hope reeks of the same chauvinism. Franklin, who graduated from Tulsa’s Booker T. Algebraists annoyed at being asked the Jacob- Washington High School. Franklin was known more son question too many times began to respond as a scholar than as a writer, although his 1947 with the question, who is the second most impor- book From Slavery to Freedom has sold millions tant ring theorist from Alabama? which is a cute of copies. He was born two days after the end of riposte but finesses a more fundamental point. 1914, which makes him almost a coeval of Gardner Is there any reason we should care to know that and Boorstin; again, I don’t know if Franklin ever Jacobson was from Alabama? Or, for that matter, met Gardner or Boorstin. know any biographical trivia about any mathemati- Gardner’s impact on mathematics in America cal figure? was profound, especially in the 1960s and 1970s, Martin Gardner, the author and mathematics when he wrote his widely popular column “Math- columnist who died in 2010, was educated in Tulsa, ematical Games” for Scientific American. I was a Oklahoma, where he was born in 1914, thereby be- fan, beginning as a teenager, and loved reading the columns, especially those in narrative form Andy Magid is George Lynn Cross Professor of Mathemat- featuring the Dr. Matrix character. I also remember ics Emeritus at the University of Oklahoma. His email with pleasure reading in Gardner’s first collection address is [email protected]. of those columns, The Scientific American Book DOI: http://dx.doi.org/10.1090/noti1091 of Mathematical Puzzles and Diversions, the MARCH 2014 NOTICES OF THE AMS 281 dedication to Gardner’s teacher at Tulsa Central platform is apparently a feature of express stops; High School, being an Oklahoma high school stu- hence the protagonist is said to live near such a dent myself at the time. I also have to say that, station) was unnecessary for most of his readers. with the possible exception of some word ladders, On the other hand, almost all the words in problem I can’t recall ever solving any of the problems in 2 are used in a specialized mathematical sense. Gardner’s column. This is no insult to Gardner—I Even if it were possible to present definition chains also never built any of the apparati described in of all the terminology involved, we would expect “The Amateur Scientist”, the wonderful Scientific years of study before a typical layperson would be American companion column by C. L. Strong—but comfortable tackling that problem. I hope those rather a testimony to his skills as a writer and the readers familiar with the terminology will agree pleasure his writing gave the reader. I suppose, with me, and I invite the rest to take my word for between the ends of the spectrum of readers like it, that the two problems are roughly the same sort me, who never solved any problems and read- of intellectual, or mathematical, challenge. ers, if any, for whom only the problems and not Month after month Martin Gardner’s column Gardner’s writing mattered fell the vast majority presented and discussed intellectual recreations of readers who made Gardner’s column the most that were on the level of what mathematicians popular feature of Scientific American in its day. thought about and yet were accessible to people Let’s agree that, whether he was a mathemati- without advanced mathematical training. He called cian or not, Martin Gardner wrote about math- these recreations—properly—mathematics. The ematical puzzles in an entertaining way that en- discipline has had no finer exponent. tranced a wide audience well beyond professional To further establish my Gardner fan credentials mathematicians and advanced students of math- before we turn to Gardner’s new book, I also re- ematics. Even when mathematics is admired by the call reading in high school with much satisfaction general public, as it was in post-Sputnik America, two other excellent Gardner books of the period, the gap between what the public thinks math- Logic Machines and Diagrams and Fads and Falla- ematics is and what mathematicians understand cies in the Name of Science. Both of these, by the mathematics to be is vast. What Martin Gardner way, could well have been collections of articles, accomplished was to bridge that gap. although they were in fact unified projects; Gard- Here’s an illustration. The following two prob- ner just seems to write that way naturally. His lems are, in my judgment, about equal in intel- other great style is being the annotator, as he is lectual content. The first comes from Gardner’s in his most popular book, The Annotated Alice in first collection of columns mentioned above. The Wonderland. To illustrate its popularity and to second is an exercise in commutative algebra. keep Gardner’s mathematician fan base in perspec- 1. A young man lives in Manhattan near a sub- tive, it’s well to recall that since its initial release way express station. He has two girlfriends, one in 1960, the number of copies of The Annotated in Brooklyn, one in the Bronx. To visit the girl in Brooklyn, he takes a train on the downtown side of Alice sold is about twenty times the number of the platform; to visit the girl in the Bronx he takes mathematicians in or joining the profession from a train on the uptown side of the same platform. then until now. Since he likes both girls equally well, he simply So how did Tulsa schoolboy Martin Gardner takes the first train that comes along. In this way become the popular and admired writer on math- he lets chance determine whether he rides to the ematics and other topics? Undiluted Hocus-Pocus: Bronx or to Brooklyn. The young man reaches the The Autobiography of Martin Gardner tells the subway platform at a random moment each Satur- story. Like everything Gardner ever wrote, it is day afternoon. Brooklyn and Bronx trains arrive at entertaining, informative, witty, deft, and a joy to the station equally often—every ten minutes. Yet read, or so this fan assesses. Mathematicians need he finds himself spending most of his time with to be aware that the role that mathematics, or the the girl in Brooklyn; in fact, on the average he goes writing of the “Mathematical Games” columns, there nine times out of ten. Can you think of a good plays in Gardner’s story of his life is brief. Readers reason why the odds so heavily favor Brooklyn? also need to be aware that Gardner is concerned 2. The commutative ring S is an algebra over the with philosophical ideas, including theological commutative ring R. The ring R has no nontrivial ones. In his preface, quoting Lenny Bruce, Gardner idempotents, and S is finitely generated as an R identifies himself with people leaving churches module. Can S have infinitely many idempotents? and going back to God. In his prologue, quoting One needs to understand some basic arithmetic himself from his 2007 Notices book review [“Do and have some notion of random and average to loops explain consciousness?: Review of I Am a solve problem one, but beyond that no special Strange Loop”, August 2007], Gardner identifies knowledge is required. I suspect that even the himself as a mysterian, i.e., one who is convinced one specialized detail that Gardner puts in (the that “no philosopher or scientist living today has uptown/downtown choice from the same central the foggiest notion of how consciousness, and its 282 NOTICES OF THE AMS VOLUME 61, NUMBER 3 inseparable companion free will, emerge, as they staff, the house my late mother-in-law grew up in surely do, from a material brain.” a mile north on Owasso, in a less ritzy area, also Gardner has previously spoken to the math- had servants’ quarters in the rear.
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