Chapter 6 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, and commerce flourished all through this region.

In Persia, for example, the reign of Khosrū Nu?īrwān,[364] the great contemporary of Justinian the law-maker, was characterized not only by an improvement in social and economic conditions, but by the cultivation of letters. Khosrū fostered learning, inviting to his court scholars from Greece, and encouraging the introduction of culture from the West as well as from the East. At this time Aristotle and Plato were translated, and portions of the Hito-padē?a, or Fables of Pilpay, were rendered from the Sanskrit into Persian. All this means that some three centuries before the great intellectual ascendancy of Bagdad a similar fostering of learning was taking place in Persia, and under pre-Mohammedan influences.

The first definite trace that we have of the introduction of the Hindu system into Arabia dates from 773 A.D.,[365] when an Indian astronomer visited the court of the caliph, bringing with him astronomical tables which at the caliph's command were translated into Arabic by Al-Fazārī.[366] Al-Khowārazmī and ?abash (A?med ibn 'Abdallāh, died c. 870) based their well-known tables upon the work of Al-Fāzarī. It may be asserted as highly probable that the numerals came at the same time as the tables. They were certainly known a few decades later, and before 825 A.D., about which time the original of the Algoritmi de numero Indorum was written, as that work makes no pretense of being the first work to treat of the Hindu numerals.

The three writers mentioned cover the period from the end of the eighth to the end of the ninth century. While the historians Al-Ma?'ūdī and Al-Bīrūnī follow quite closely upon the men mentioned, it is well to note again the Arab writers on Hindu arithmetic, contemporary with Al-Khowārazmī, who were mentioned in chapter I, viz. Al-Kindī, Sened ibn 'Alī, and Al-?ūfī.

For over five hundred years Arabic writers and others continued to apply to works on arithmetic the name "Indian." In the tenth century such writers are 'Abdallāh ibn al-?asan, Abū 'l-Qāsim[367] (died 987 A.D.) of Antioch, and Mo?ammed ibn 'Abdallāh, Abū Na?r[368] (c. 982), of Kalwādā near Bagdad. Others of the same period or earlier (since they are mentioned in the Fihrist,[369] 987 A.D.), who explicitly use the word "Hindu" or "Indian," are Sinān ibn al-Fat?[370] of ?arrān, and Ahmed ibn 'Omar, al-Karābīsī.[371] In the eleventh century come Al-Bīrūnī[372] (973-1048) and 'Ali ibn A?med, Abū 'l-?asan, Al-Nasawī[373] (c. 1030). The following century brings similar works by Ishāq ibn Yūsuf al-?ardafī[374] and Samū'īl ibn Ya?yā ibn 'Abbās al-Ma?rebī al-Andalusī[375] (c. 1174), and in the thirteenth century are 'Abdallatīf ibn Yūsuf ibn Mo?ammed, Muwaffaq al-Dīn Abū Mo?ammed al-Ba?dādī[376] (c. 1231), and Ibn al-Bannā.[377]

The Greek monk Maximus Planudes, writing in the first half of the fourteenth century, followed the Arabic usage in calling his work Indian Arithmetic.[378] There were numerous other Arabic writers upon arithmetic, as that subject occupied one of the high places among the sciences, but most of them did not feel it necessary to refer to the origin of the symbols, the knowledge of which might well have been taken for granted.

One document, cited by Woepcke,[379] is of special interest since it shows at an early period, 970 A.D., the use of the ordinary Arabic forms alongside the ?obār. The title of the work is Interesting and Beautiful Problems on Numbers copied by A?med ibn Mo?ammed ibn 'Abdaljalīl, Abū Sa'īd, al-Sijzī,[380] (951-1024) from a work by a priest and physician, Na?īf ibn Yumn,[381] al-Qass (died c. 990). Suter does not mention this work of Na?īf.

The second reason for not ascribing too much credit to the purely Arab influence is that the Arab by himself never showed any intellectual strength. What took place after Mo?ammed had lighted the fire in the hearts of his people was just what always takes place when different types of strong races blend,-a great renaissance in divers lines. It was seen in the blending of such types at Miletus in the time of Thales, at Rome in the days of the early invaders, at Alexandria when the Greek set firm foot on Egyptian soil, and we see it now when all the nations mingle their vitality in the New World. So when the Arab culture joined with the Persian, a new civilization rose and flourished.[382] The Arab influence came not from its purity, but from its intermingling with an influence more cultured if less virile.

As a result of this interactivity among peoples of diverse interests and powers, Mohammedanism was to the world from the eighth to the thirteenth century what Rome and Athens and the Italo-Hellenic influence generally had been to the ancient civilization. "If they did not possess the spirit of invention which distinguished the Greeks and the Hindus, if they did not show the perseverance in their observations that characterized the Chinese astronomers, they at least possessed the virility of a new and victorious people, with a desire to understand what others had accomplished, and a taste which led them with equal ardor to the study of algebra and of poetry, of philosophy and of language."[383]

It was in 622 A.D. that Mo?ammed fled from Mecca, and within a century from that time the crescent had replaced the cross in Christian Asia, in Northern Africa, and in a goodly portion of Spain. The Arab empire was an ellipse of learning with its foci at Bagdad and Cordova, and its rulers not infrequently took pride in demanding intellectual rather than commercial treasure as the result of conquest.[384]

It was under these influences, either pre-Mohammedan or later, that the Hindu numerals found their way to the North. If they were known before Mo?ammed's time, the proof of this fact is now lost. This much, however, is known, that in the eighth century they were taken to Bagdad. It was early in that century that the Mohammedans obtained their first foothold in northern India, thus foreshadowing an epoch of supremacy that endured with varied fortunes until after the golden age of Akbar the Great (1542-1605) and Shah Jehan. They also conquered Khorassan and Afghanistan, so that the learning and the commercial customs of India at once found easy access to the newly-established schools and the bazaars of Mesopotamia and western Asia. The particular paths of conquest and of commerce were either by way of the Khyber Pass and through Kabul, Herat and Khorassan, or by sea through the strait of Ormuz to Basra (Busra) at the head of the Persian Gulf, and thence to Bagdad. As a matter of fact, one form of Arabic numerals, the one now in use by the Arabs, is attributed to the influence of Kabul, while the other, which eventually became our numerals, may very likely have reached Arabia by the other route. It is in Bagdad,[385] Dār al-Salām-"the Abode of Peace," that our special interest in the introduction of the numerals centers. Built upon the ruins of an ancient town by Al-Man?ūr[386] in the second half of the eighth century, it lies in one of those regions where the converging routes of trade give rise to large cities.[387] Quite as well of Bagdad as of Athens might Cardinal Newman have said:[388]

"What it lost in conveniences of approach, it gained in its neighborhood to the traditions of the mysterious East, and in the loveliness of the region in which it lay. Hither, then, as to a sort of ideal land, where all archetypes of the great and the fair were found in substantial being, and all departments of truth explored, and all diversities of intellectual power exhibited, where taste and philosophy were majestically enthroned as in a royal court, where there was no sovereignty but that of mind, and no nobility but that of genius, where professors were rulers, and princes did homage, thither flocked continually from the very corners of the orbis terrarum the many-tongued generation, just rising, or just risen into manhood, in order to gain wisdom." For here it was that Al-Man?ūr and Al-Māmūn and Hārūn al-Rashīd (Aaron the Just) made for a time the world's center of intellectual activity in general and in the domain of mathematics in particular.[389] It was just after the Sindhind was brought to Bagdad that Mo?ammed ibn Mūsā al-Khowārazmī, whose name has already been mentioned,[390] was called to that city. He was the most celebrated mathematician of his time, either in the East or West, writing treatises on arithmetic, the sundial, the astrolabe, chronology, geometry, and algebra, and giving through the Latin transliteration of his name, algoritmi, the name of algorism to the early arithmetics using the new Hindu numerals.[391] Appreciating at once the value of the position system so recently brought from India, he wrote an arithmetic based upon these numerals, and this was translated into Latin in the time of Adelhard of Bath (c. 1180), although possibly by his contemporary countryman Robert Cestrensis.[392] This translation was found in Cambridge and was published by Boncompagni in 1857.[393]

Contemporary with Al-Khowārazmī, and working also under Al-Māmūn, was a Jewish astronomer, Abū 'l-?eiyib, Sened ibn 'Alī, who is said to have adopted the Mohammedan religion at the caliph's request. He also wrote a work on Hindu arithmetic,[394] so that the subject must have been attracting considerable attention at that time. Indeed, the struggle to have the Hindu numerals replace the Arabic did not cease for a long time thereafter. 'Alī ibn A?med al-Nasawī, in his arithmetic of c. 1025, tells us that the symbolism of number was still unsettled in his day, although most people preferred the strictly Arabic forms.[395]

We thus have the numerals in Arabia, in two forms: one the form now used there, and the other the one used by Al-Khowārazmī. The question then remains, how did this second form find its way into Europe? and this question will be considered in the next chapter.

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