either in his time or at any time before they definitely
appeared in the tenth century. These centuries, five in number, represented
the darkest of the Dark Ages, and even if these numerals were occasionally
met and studied, no trace of them would be likely to show itself in the
{90} literature of the period, unless by chance it should get into the
writings of some man like Alcuin. As a matter of fact, it was not until the
ninth or tenth century that there is any tangible evidence of their
presence in Christendom. They were probably known to merchants here and
there, but in their incomplete state they were not of sufficient importance
to attract any considerable attention.

As a result of this brief survey of the evidence several conclusions seem
reasonable: (1) commerce, and travel for travel's sake, never died out
between the East and the West; (2) merchants had every opportunity of
knowing, and would have been unreasonably stupid if they had not known, the
elementary number systems of the peoples with whom they were trading, but
they would not have put this knowledge in permanent written form; (3)
wandering scholars would have known many and strange things about the
peoples they met, but they too were not, as a class, writers; (4) there is
every reason a priori for believing that the [.g]ob[=a]r numerals would
have been known to merchants, and probably to some of the wandering
scholars, long before the Arabs conquered northern Africa; (5) the wonder
is not that the Hindu-Arabic numerals were known about 1000 A.D., and that
they were the subject of an elaborate work in 1202 by Fibonacci, but rather
that more extended manuscript evidence of their appearance before that time
has not been found. That they were more or less known early in the Middle
Ages, certainly to many merchants of Christian Europe, and probably to
several scholars, but without the zero, is hardly to be doubted. The lack
of documentary evidence is not at all strange, in view of all of the
circumstances.

* * * * *

{91}

CHAPTER VI

THE DEVELOPMENT OF THE NUMERALS AMONG THE ARABS

If the numerals had their origin in India, as seems most probable, when did
the Arabs come to know of them? It is customary to say that it was due to
the influence of Mohammedanism that learning spread through Persia and
Arabia; and so it was, in part. But learning was already respected in these
countries long before Mohammed appeared,