Rithmomachy (or Rithmomachia, also Arithmomachia, Rythmomachy, Rhythmomachy, or sundry other variants; sometimes known as The Philosophers' Game) is an 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".

Virtually nothing 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 appears in literature. Based as it is upon the Greek theory of numbers, appearing as it does with 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 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.

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, circles, and pyramids. 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.

There were a variety of capture methods. For example one piece could capture another with the same number by landing on it. Another method was to capture a piece by occupying all of the positions that piece could move to.

There were also a variety of victory conditions for determining when a game would end and who the winner was. For example one condition required placing pieces in linear arrangements whose numbers formed various type of numerical progression. The types of progression required, arithmetic, geometric and harmonic, suggest a connection with the mathematical work of Boethius.

From the seventeenth century onwards the game, which at its peak rivaled chess for popularity in Europe, virtually disappeared until the late 19th and early 20th century when rediscovered by historians.

Further Reading

The Philosopher's Game, Ann E Moyer, University of Michigan Press, ISBN 0472112287

Das mittelalterliche Zahlenkampfspiel, Arno Borst, ISBN 3825337502