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Rithmomachy (or Rithmomachia, also Arithmomachia, Rythmomachy, Rhythmomachy, or sundry other variants; sometimes known as The Philosophers' Game) is a highly complex, early European mathematical board game. The earliest known description of it dates from the eleventh century. A literal translation of the name is "The Battle of the Numbers". The game is much like chess, except most methods of capture depend on the numbers inscribed on each piece.
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It has been argued that between the twelfth and sixteenth centuries, "rithmomachia served as a practical exemplar for teaching the contemplative values of Boethian mathematical philosophy, which emphasized the natural harmony and perfection of number and proportion. The game, Moyer argues, was used both as a mnemonic drill for the study of Boethian number theory and, more importantly, as a vehicle for moral education, by reminding players of the mathematical harmony of creation."
History
Very little, if anything, is known about the origin of the game. But it is known that medieval writers attributed it to Pythagoras, although no trace of it has been discovered in Greek literature, and the earliest mention of it is from the time of Hermannus Contractus (1013–1054).
The name, which appears in a variety of forms, points to a Greek origin, the more so because Greek was little known at the time when the game first appeared in literature. Based upon the Greek theory of numbers, and having a Greek name, it is still speculated by some that the origin of the game is to be sought in the Greek civilization, and perhaps in the later schools of Byzantium or Alexandria.
The first written evidence of Rithmomachia dates back to around 1030, when a monk, named Asilo, created a game that illustrated the number theory of Boëthius' De institutione arithmetica, for the students of monastery schools. The rules of the game were improved shortly thereafter by the respected monk, Hermannus Contractus, from Reichenau, and in the school of Liège. In the following centuries, Rithmomachia spread quickly through schools and monasteries in the southern parts of Germany and France. It was used mainly as a teaching aid, but, gradually, intellectuals started to play it for pleasure. In the 13th century Rithmomachia came to England, where famous mathematician Thomas Bradwardine wrote a text about it. Even Roger Bacon recommended Rithmomachia to his students, while Sir Thomas More let the inhabitants of the fictitious Utopia play it for recreation.
The game was well enough known as to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century, and to have public advertisements of the sale of the board and pieces under the shadow of the old Sorbonne.
Gameplay
The game was played on a board resembling the one used for chess or checkers, with eight squares on the shorter side, but with sixteen on the longer side. The forms used for the pieces were triangles, squares, and rounds. Pyramids could be formed by stacking pieces. The game was noteworthy in that the black and white forces were not symmetrical. Although each side had the same array of pieces, the numbers on them differed, allowing different possible captures and winning configurations to the two players.
The rules below describe the most common version of the game, played through much of the Middle Ages and Renaissance. There was also a variant propounded by Fulke in the 16th century, with significantly different (and somewhat more consistent) capture rules.
Pieces
There are four types of pieces, which are Rounds, Triangles, Squares, and Pyramids.
Capturing
There were a variety of capture methods. Pieces do not land on another piece to capture it, but instead remain in their square and remove the other. If a piece is captured, it changes sides.
Victory
There were also a variety of victory conditions for determining when a game would end and who the winner was. There were common victories, and proper victories, which were recommended for more skilled players. Proper victories required placing pieces in linear arrangements in the opponent's side of the board, with the numbers formed by the arrangement following various types of numerical progression. The types of progression required — arithmetic, geometric and harmonic — suggest a connection with the mathematical work of Boëthius.
Popularity
At its peak, Rithmomachy rivalled chess for popularity in Europe. The game virtually disappeared from the 17th century until the late 19th and early 20th century, when it was rediscovered by historians.