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The Philosophers' Game: Rithmomachia in Medieval and Renaissance Europe, with an edition of Ralph Lever and William Fulke, "The Most Noble, Auncient, and Learned Playe" (1563)

Ann E. Moyer
University of Michigan Press
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
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Rithmomachia. Say it with me, boys and girls: Rith-mo-mach-i-a. It's a game, sort of like chess but involving arithmetic. According to Thomas More, that's what they play in Utopia instead of "gambling with dice or other such ruinous games." That and a game about the contest between vices and virtues.

The game is played on an elongated chessboard. The pieces have numbers on them, chosen so that their ratios will exemplify the various categories of ratio discussed in Boethius' Arithmetic. Pieces are captured by setting up various arithmetical identities, so to play the game one has to be able to do mental calculation. The details of the rules varied, but the basic idea was always the same.

Sound boring? Well, I guess it does. But rithmomachia seems to have been quite popular with — or at least was played by — educated men in Northern Europe for 500 years, between the 11th and the 16th century. Whether they actually enjoyed it or just used it as a way to sharpen their arithmetic skills is anyone's guess.

Ann Moyer's book The Philosophers' Game is an account of rithmomachia and its connection to the teaching of arithmetic in the tradition of Boethius' book (which is in turn based on Nichomachus' Introduction to Arithmetic, so is a descendent of Pythagoreanism). It also includes an edition of one of the various books describing the game and its rules. (So if any of you out there is thinking of using the game to torture students, here's your chance.) Moyer thinks that the link between the game and Boethius is very important, and that the game started to lose its appeal exactly when the newer approaches to arithmetic and algebra began to become prevalent in the 16th and 17th centuries. The book has the potential to be the source of various interesting student activities or projects; consider asking your library to get a copy.

Fernando Q. Gouvêa ( reads science fiction, teaches at Colby College, edits FOCUS and MAA Online, and writes books, including, most recently, Math through the Ages, with William Berlinghoff.

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