accordingly looked upon as a saint,[[282]] his bones were enshrined,[[283]] and as a natural consequence his books were among the classics in the church schools for a thousand years.[[284]] It is pathetic, however, to think of the medieval student trying to extract mental nourishment from a work so abstract, so meaningless, so unnecessarily complicated, as the arithmetic of Boethius.
He was looked upon by his contemporaries and immediate successors as a master, for Cassiodorus[[285]] (c. 490-c. 585 A.D.) says to him: "Through your translations the music of Pythagoras and the astronomy of Ptolemy are read by those of Italy, and the arithmetic of Nicomachus and the geometry of Euclid are known to those of the West."[[286]] Founder of the medieval scholasticism,
distinguishing the trivium and quadrivium,[[287]] writing the only classics of his time, Gibbon well called him "the last of the Romans whom Cato or Tully could have acknowledged for their countryman."[[288]]
The second question relating to Boethius is this: Could he possibly have known the Hindu numerals? In view of the relations that will be shown to have existed between the East and the West, there can only be an affirmative answer to this question. The numerals had existed, without the zero, for several centuries; they had been well known in India; there had been a continued interchange of thought between the East and West; and warriors, ambassadors, scholars, and the restless trader, all had gone back and forth, by land or more frequently by sea, between the Mediterranean lands and the centers of Indian commerce and culture. Boethius could very well have learned one or more forms of Hindu numerals from some traveler or merchant.
To justify this statement it is necessary to speak more fully of these relations between the Far East and Europe. It is true that we have no records of the interchange of learning, in any large way, between eastern Asia and central Europe in the century preceding the time of Boethius. But it is one of the mistakes of scholars to believe that they are the sole transmitters of knowledge.
As a matter of fact there is abundant reason for believing that Hindu numerals would naturally have been known to the Arabs, and even along every trade route to the remote west, long before the zero entered to make their place-value possible, and that the characters, the methods of calculating, the improvements that took place from time to time, the zero when it appeared, and the customs as to solving business problems, would all have been made known from generation to generation along these same trade routes from the Orient to the Occident. It must always be kept in mind that it was to the tradesman and the wandering scholar that the spread of such learning was due, rather than to the school man. Indeed, Avicenna[[289]] (980-1037 A.D.) in a short biography of himself relates that when his people were living at Bokhāra his father sent him to the house of a grocer to learn the Hindu art of reckoning, in which this grocer (oil dealer, possibly) was expert. Leonardo of Pisa, too, had a similar training.
The whole question of this spread of mercantile knowledge along the trade routes is so connected with the ġobār numerals, the Boethius question, Gerbert, Leonardo of Pisa, and other names and events, that a digression for its consideration now becomes necessary.[[290]]
Even in very remote times, before the Hindu numerals were sculptured in the cave of Nānā Ghāt, there were trade relations between Arabia and India. Indeed, long before the Aryans went to India the great Turanian race had spread its civilization from the Mediterranean to the Indus.[[291]] At a much later period the Arabs were the intermediaries between Egypt and Syria on the west, and the farther Orient.[[292]] In the sixth century B.C., Hecatæus,[[293]] the father of geography, was acquainted not only with the Mediterranean lands but with the countries as far as the Indus,[[294]] and in Biblical times there were regular triennial voyages to India. Indeed, the story of Joseph bears witness to the caravan trade from India, across Arabia, and on to the banks of the Nile. About the same time as Hecatæus, Scylax, a Persian admiral under Darius, from Caryanda on the coast of Asia Minor, traveled to
northwest India and wrote upon his ventures.[[295]] He induced the nations along the Indus to acknowledge the Persian supremacy, and such number systems as there were in these lands would naturally have been known to a man of his attainments.