The intersection between the set of all mathematicians and the set of chess players is not only anything but empty, it is partitioned into cells indexed by, well, how about “degree of commitment to the game”? There are masters and even grandmasters among the mathematicians, and some obvious names spring to mind immediately, such as Lasker and Euwe. Our fellow travelers the quantum mechanics pioneers also had chess players among them, as illustrated by a famous letter exchange between Heisenberg and Dirac concerning the possibility of giving checkmate with a certain set of pieces (was it rook and knight? — I don’t recall).
On a personal note I recall vividly that at UCLA in the late 1970s the faculty and graduate student lounge in the Mathematics Department sported a completely outfitted chess-table, and a friend of mine once interrupted Robert Steinberg in a game to ask him a question: Steinberg didn’t even break stride and just mumbled that it had to do with the Artin conjecture and continued with his game. Moreover, when I was still a high school student, my favorite Mathematics teacher had a standing offer of an A grade for any student who could beat him at chess, which I never did. I guess he would be classed as among the more committed players.
Another nonempty intersection of note is that between the set of mathematicians and the set of detective story aficionados, with added criteria thrown in along the lines of, e.g., Agatha Christie vs. Rex Stout vs. Arthur Conan Doyle vs. Dorothy L. Sayers vs. G. K. Chesterton vs. even John Le Carré. And it is of course true, too, that the three sets in question meet, and I, for one, am very happy to live in this intersection of all three classes: I love chess (but not too much, lest it take over!), and I love detective fiction (but also at a proper distance). And I guess this characterization ultimately describes a lot of us, clearly including none other than the logician Raymond Smullyan, the author of the book under review.
Indeed, the indicated “50 tantalizing problems of chess detection” are presented in the setting or context of what I guess is describable as part of the Sherlockian apocrypha, although the focus is really on chess not crime. The problems are often of retrograde type (loosely meaning that a given position on the chessboard should present the occasion for deduction of what must have happened to get there), are laden with cleverness, and are fun to read if only because Smullyan takes great pains to couch the whole business in the right idiom: it’s Dr. Watson narrating and Holmes posing the problems, replete with characters from the opus appearing on the scene, and Victorian London coming to life on the page once again.
Thus, The Chess Mysteries of Sherlock Holmes are a wonderful diversion on a number of counts, including the sheer irresistibility of once again being transported to the 221B Baker Street and its environs. Of course, with Smullyan holding the pen, the puzzles are logical gems in their own right, so if this sort of thing is your cup of tea, then, indeed, the game is afoot!
Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.