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 Khosr[=u]
Nu['s][=i]rw[=a]n,[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. Khosr[=u] 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-pad[=e]['s]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.
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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-Faz[=a]r[=i].[366] Al-Khow[=a]razm[=i] and [H.]abash (A[h.]med ibn
`Abdall[=a]h, died c. 870) based their well-known tables upon the work of
Al-F[=a]zar[=i]. 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['s]`[=u]d[=i] and
Al-B[=i]r[=u]n[=i] follow quite closely upon the men mentioned, it is well
to note again the Arab writers on Hindu arithmetic, contemporary with
Al-Khow[=a]razm[=i], who were mentioned in chapter I, viz. Al-Kind[=i],
Sened ibn `Al[=i], and Al-[S.][=u]f[=i].
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 `Abdall[=a]h ibn al-[H.]asan, Ab[=u] 'l-Q[=a]sim[367] (died 987 A.D.)
of Antioch, and Mo[h.]ammed ibn `Abdall[=a]h, Ab[=u] Na[s.]r[368] (c. 982),
of Kalw[=a]d[=a] near Bagdad. Others of the same period or {93} earlier
(since they are mentioned in the _Fihrist_,[369] 987 A.D.), who explicitly
use the word "Hindu" or "Indian," are Sin[=a]n ibn al-Fat[h.][370] of
[H.]arr[=a]n, and Ahmed ibn `Omar, al-Kar[=a]b[=i]s[=i].[371] In the
eleventh century come Al-B[=i]r[=u]n[=i][372] (973-1048) and `Ali ibn
A[h.]med, Ab[=u] 'l-[H.]asan, Al-Nasaw[=i][373] (c. 1030). The following
century brings similar works by Ish[=a]q ibn Y[=u]suf al-[S.]ardaf[=i][374]
and Sam[=u]'[=i]l ibn Ya[h.]y[=a] ibn `Abb[=a]s al-Ma[.g]reb[=i]
al-Andalus[=i][375] (c. 1174), and in the thirteenth century are
`Abdallat[=i]f ibn Y[=u]suf ibn Mo[h.]ammed, Muwaffaq al-D[=i]n Ab[=u]
Mo[h.]ammed al-Ba[.g]d[=a]d[=i][376] (c. 1231), and Ibn al-Bann[=a].[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.
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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 [.g]ob[=a]r. The title of the work is _Interesting and
Beautiful Problems on Numbers_ copied by A[h.]med ibn Mo[h.]ammed ibn
`Abdaljal[=i]l, Ab[=u] Sa`[=i]d, al-Sijz[=i],[380] (951-1024) from a work
by a priest and physician, Na[z.][=i]f ibn Yumn,[381] al-Qass (died c.
990). Suter does not mention this work of Na[z.][=i]f.
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[h.]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
{95} 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[h.]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[h.]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 {96} 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] D[=a]r
al-Sal[=a]m--"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[s.][=u]r[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 {97} 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[s.][=u]r and
Al-M[=a]m[=u]n and H[=a]r[=u]n al-Rash[=i]d (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[h.]ammed ibn M[=u]s[=a] al-Khow[=a]razm[=i],
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-Khow[=a]razm[=i], and working also under
Al-M[=a]m[=u]n, was a Jewish astronomer, Ab[=u] 'l-[T.]eiyib, {98} Sened
ibn `Al[=i], 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. `Al[=i] ibn A[h.]med al-Nasaw[=i], 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-Khow[=a]razm[=i]. 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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