A MEDIEVAL MATHEMATICAL MANUSCRIPT

The medieval cleric Alcuin (AD 735–804) is credited in surviving manuscripts with being the originator of a collection of fifty-three mathematical and logical puzzles, the Propositiones ad acuendos iuvenes (‘Problems for Sharpening the Young’). There is no direct evidence to connect the collection with Alcuin either as compiler or creator, but even modern commentators continue to associate his name with the puzzles. There are at least fourteen extant or partial copies of the Propositiones, which date from the ninth to the fifteenth century, suggesting that the collection was in popular use at least from the time of Alcuin onwards. Michael Gorman confidently listed the Propositiones among ninety spurious prose works of Alcuin for two reasons: firstly, because Alcuin always attached a dedicatory letter to his works, and there is none here, and secondly, because the work falls, Gorman thinks, among those documents which Alcuin would have had neither the time nor the energy to write in the period AD 782–800. Alcuin himself admitted to having only ‘stolen hours’ at night in which to write a life of Willibrord. Despite Gorman's view that the work is pseudo-Alcuin, it is reasonable to ask if there is internal evidence in the puzzles which would support or oppose the assigning of the collection to Alcuin himself, committed as he was to the promotion of educational subjects, including mathematics, in the course of the Carolingian ‘renaissance’.

The majority of the problem types in the Propositiones are known from earlier Chinese, Indian, Egyptian, Byzantine, Greek, and Roman sources, whilst others appear in works by Boethius, Metrodorus, and Isidore of Seville. Among the puzzles, however, there are a small number of important types that are not as yet known from earlier sources. These include the so-called ‘river-crossing problems’, ‘strange family problems’, a transportation (or ‘desert-crossing’) problem, and a problem that relies on the summation of an arithmetical series. The case for the mathematical creativity of the author, if there was only one author, rests on these. One puzzle has outstripped all the others in having popular appeal down to the present day. This puzzle, passing presumably from later medieval reproductions of the Propositiones into oral tradition, concerns a farmer who needs to ferry three items across a river in a boat.