"caracteres," a word used by Radulph of Laon in the same sense a century later.[[447]] It is probable that Gerbert was the first to describe these ġobār numerals in any scientific way in Christian Europe, but without the zero. If he knew the latter he certainly did not understand its use.[[448]]
The question still to be settled is as to where he found these numerals. That he did not bring them from Spain is the opinion of a number of careful investigators.[[449]] This is thought to be the more probable because most of the men who made Spain famous for learning lived after Gerbert was there. Such were Ibn Sīnā (Avicenna) who lived at the beginning, and Gerber of Seville who flourished in the middle, of the eleventh century, and Abū Roshd (Averroës) who lived at the end of the twelfth.[[450]] Others hold that his proximity to
the Arabs for three years makes it probable that he assimilated some of their learning, in spite of the fact that the lines between Christian and Moor at that time were sharply drawn.[[451]] Writers fail, however, to recognize that a commercial numeral system would have been more likely to be made known by merchants than by scholars. The itinerant peddler knew no forbidden pale in Spain, any more than he has known one in other lands. If the ġobār numerals were used for marking wares or keeping simple accounts, it was he who would have known them, and who would have been the one rather than any Arab scholar to bring them to the inquiring mind of the young French monk. The facts that Gerbert knew them only imperfectly, that he used them solely for calculations, and that the forms are evidently like the Spanish ġobār, make it all the more probable that it was through the small tradesman of the Moors that this versatile scholar derived his knowledge. Moreover the part of the geometry bearing his name, and that seems unquestionably his, shows the Arab influence, proving that he at least came into contact with the transplanted Oriental learning, even though imperfectly.[[452]] There was also the persistent Jewish merchant trading with both peoples then as now, always alive to the acquiring of useful knowledge, and it would be very natural for a man like Gerbert to welcome learning from such a source.
On the other hand, the two leading sources of information as to the life of Gerbert reveal practically nothing to show that he came within the Moorish sphere of influence during his sojourn in Spain. These sources
are his letters and the history written by Richer. Gerbert was a master of the epistolary art, and his exalted position led to the preservation of his letters to a degree that would not have been vouchsafed even by their classic excellence.[[453]] Richer was a monk at St. Remi de Rheims, and was doubtless a pupil of Gerbert. The latter, when archbishop of Rheims, asked Richer to write a history of his times, and this was done. The work lay in manuscript, entirely forgotten until Pertz discovered it at Bamberg in 1833.[[454]] The work is dedicated to Gerbert as archbishop of Rheims,[[455]] and would assuredly have testified to such efforts as he may have made to secure the learning of the Moors.
Now it is a fact that neither the letters nor this history makes any statement as to Gerbert's contact with the Saracens. The letters do not speak of the Moors, of the Arab numerals, nor of Cordova. Spain is not referred to by that name, and only one Spanish scholar is mentioned. In one of his letters he speaks of Joseph Ispanus,[[456]] or Joseph Sapiens, but who this Joseph the Wise of Spain may have been we do not know. Possibly
it was he who contributed the morsel of knowledge so imperfectly assimilated by the young French monk.[[457]] Within a few years after Gerbert's visit two young Spanish monks of lesser fame, and doubtless with not that keen interest in mathematical matters which Gerbert had, regarded the apparently slight knowledge which they had of the Hindu numeral forms as worthy of somewhat permanent record[[458]] in manuscripts which they were transcribing. The fact that such knowledge had penetrated to their modest cloisters in northern Spain—the one Albelda or Albaida—indicates that it was rather widely diffused.
Gerbert's treatise Libellus de numerorum divisione[[459]] is characterized by Chasles as "one of the most obscure documents in the history of science."[[460]] The most complete information in regard to this and the other mathematical works of Gerbert is given by Bubnov,[[461]] who considers this work to be genuine.[[462]]
So little did Gerbert appreciate these numerals that in his works known as the Regula de abaco computi and the Libellus he makes no use of them at all, employing only the Roman forms.[[463]] Nevertheless Bernelinus[[464]] refers to the nine ġobār characters.[[465]] These Gerbert had marked on a thousand jetons or counters,[[466]] using the latter on an abacus which he had a sign-maker prepare for him.[[467]] Instead of putting eight counters in say the tens' column, Gerbert would put a single counter marked 8, and so for the other places, leaving the column empty where we would place a zero, but where he, lacking the zero, had no counter to place. These counters he possibly called caracteres, a name which adhered also to the figures themselves. It is an interesting speculation to consider whether these apices, as they are called in the Boethius interpolations, were in any way suggested by those Roman jetons generally known in numismatics as tesserae, and bearing the figures I-XVI, the sixteen referring to the number of assi in a sestertius.[[468]] The