Rithmomachia

David Sepkoski wrote 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, that it 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.

"[2] The game declined sharply in popularity in the 17th century, as it was no longer used in education, and potential players were not introduced to it during their schooling.

The first written evidence of Rithmomachia dates to around 1030, when a monk named Asilo (probably the future Bishop Adalbero of Würzburg)[3] created a game that illustrated the number theory of Boethius' De institutione arithmetica, for the students of monastery schools.

De institutione arithmetica was the standard textbook for instruction in arithmetics in the period for those lucky enough to receive a medieval education.

The rules of the game were improved and spelled out more shortly thereafter by another monk, Hermannus Contractus (1013–1054) from Reichenau, and in the school of Liège.

Even Roger Bacon recommended Rithmomachia to his students, while Sir Thomas More let the inhabitants described in the book Utopia play it for recreation.

The game was known well enough to justify printed treatises in Latin, French, Italian, and German, in the sixteenth century.

In 1572 Francesco Barozzi published a version in Venice which was translated into German by Augustus II, Duke of Brunswick.

The types of progression required — arithmetic, geometric and harmonic — fit with the mathematical and numerological teachings of Boethius.