Rithmomachia
A medieval mathematical board game for teaching number theory.
Rithmomachia, also called the philosophers' game or the battle of the numbers, is an early European board game based on mathematics. Its first known description appears in the eleventh century. The name, derived loosely from Greek, means "The Battle of the Numbers." The game resembles chess, but most captures depend on the numbers written on the pieces. Teachers used it as a tool for instructing arithmetic, part of the quadrivium in medieval Western European classical education.
The game's origins are obscure. Medieval writers credited Pythagoras, but no Greek source mentions it. The earliest surviving references come from the early 1000s, suggesting it was invented in the late tenth or early eleventh century. The Greek name may indicate a creator with a rare classical education in Greek, or a genuine origin in Greece or the Byzantine Empire. The first written evidence dates to around 1030, when a monk named Asilo (likely the future Bishop Adalbero of Würzburg) designed a game illustrating the number theory in Boethius's *De institutione arithmetica*, the standard arithmetic textbook of the time. Another monk, Hermannus Contractus (1013–1054) of Reichenau, and the school of Liège soon refined and recorded the rules. Over the following centuries, Rithmomachia spread through schools and monasteries in southern Germany and France. It was mainly a teaching aid, but intellectuals eventually played it for enjoyment. In the thirteenth century, it reached England, where mathematician Thomas Bradwardine wrote about it. Roger Bacon recommended it to his students, and Thomas More included it as a recreation for the inhabitants of Utopia. By the sixteenth century, printed treatises existed in Latin, French, Italian, and German. Two advertisements for game sets survive, one from Paris (1556) and another from London (1563). Several playing boards from the medieval and early modern periods have survived, providing valuable archaeological evidence of the game's use.
- Earliest known description
- 11th century
- First written evidence
- circa 1030
- Peak popularity
- 16th century
- Decline
- 17th century
- Field
- Mathematical board game
- Known for
- Educational tool for Boethian number theory
Lore & Background
Little is known about the origin of the game. Medieval writers attributed it to Pythagoras, but no trace of it has been discovered in Greek literature. The earliest surviving mentions are from the early 11th century, suggesting it was created in the late 10th or early 11th century. The name and its many variations are from Greek; it is unclear whether this was due to being created by a rare Western European with a classical education that involved learning Greek, or if the game had a genuine origin in Greece and the Greek-speaking Byzantine Empire of the period. The first written evidence dates to around 1030, when a monk named Asilo (probably the future Bishop Adalbero of Würzburg) created a game that illustrated the number theory of Boethius' De institutione arithmetica, for the students of monastery schools. Contrary to earlier claims, several physical boards from the medieval and early modern periods have been discovered, confirming the game's historical presence.
Reader's Guide
Rithmomachia was at its most popular in the 16th century. The Tudor polymath, statesman and publisher of the Geneva Bible, Sir Rowland Hill, published on the game under the title 'The most ancient and learned Playe, called the Philosopher's Game' in 1562; his house at Soulton Hall also contains a board for the game on a basement parlour or prayer room. In 1572 Francesco Barozzi published a version in Venice which was translated into German by Augustus II, Duke of Brunswick. It lost its popularity sharply in the 17th century, virtually disappearing as the style of teaching mathematics changed, and Boethius's mathematics was considered old-fashioned and obsolete. One issue was that the rules were never standardized, with major variations from teacher to teacher. The game partially survived by clinging to the now far more popular chess. Gustavus Selenus included the rules of rithmomachia as an appendix in one of his books on chess, and the game persisted as 'arithmetic chess' or 'numerical checkers' as a side mention in German chess books for some time afterward, a curiosity but a rarely-played one. The game was rediscovered in the 20th century by historians of board games such as Arno Borst.
Did You Know?
- The game was used as an educational tool for teaching arithmetic as part of the quadrivium.
- No archaeological evidence of the game (such as playing boards) has survived from the medieval and early modern periods.
- The white pyramid is made of pieces totaling 91, while the black pyramid totals 190.
- Victory conditions included proper victories requiring linear arrangements following arithmetic, geometric, and harmonic progressions.
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