The Hindu-Arabic Numerals | Page 3

changed more or less from century to century. Even to-day the number
of methods of expressing numerical concepts is much greater than one
would believe before making a study of the subject, for the idea that
our common numerals are universal is far from being correct. It will be
well, then, to think of the numerals that we still commonly call Arabic,
as only one of many systems in use just before the Christian era. As it
then existed the system was no better than many others, it was of late
origin, it contained no zero, it was cumbersome and little used, {2} and
it had no particular promise. Not until centuries later did the system
have any standing in the world of business and science; and had the

place value which now characterizes it, and which requires a zero, been
worked out in Greece, we might have been using Greek numerals
to-day instead of the ones with which we are familiar.
Of the first number forms that the world used this is not the place to
speak. Many of them are interesting, but none had much scientific
value. In Europe the invention of notation was generally assigned to the
eastern shores of the Mediterranean until the critical period of about a
century ago,--sometimes to the Hebrews, sometimes to the Egyptians,
but more often to the early trading Phoenicians.[1]
The idea that our common numerals are Arabic in origin is not an old
one. The mediæval and Renaissance writers generally recognized them
as Indian, and many of them expressly stated that they were of Hindu
origin.[2] {3} Others argued that they were probably invented by the
Chaldeans or the Jews because they increased in value from right to left,
an argument that would apply quite as well to the Roman and Greek
systems, or to any other. It was, indeed, to the general idea of notation
that many of these writers referred, as is evident from the words of
England's earliest arithmetical textbook-maker, Robert Recorde (c.
1542): "In that thinge all men do agree, that the Chaldays, whiche
fyrste inuented thys arte, did set these figures as thei set all their letters.
for they wryte backwarde as you tearme it, and so doo they reade. And
that may appeare in all Hebrewe, Chaldaye and Arabike bookes ...
where as the Greekes, Latines, and all nations of Europe, do wryte and
reade from the lefte hand towarde the ryghte."[3] Others, and {4}
among them such influential writers as Tartaglia[4] in Italy and
Köbel[5] in Germany, asserted the Arabic origin of the numerals, while
still others left the matter undecided[6] or simply dismissed them as
"barbaric."[7] Of course the Arabs themselves never laid claim to the
invention, always recognizing their indebtedness to the Hindus both for
the numeral forms and for the distinguishing feature of place value.
Foremost among these writers was the great master of the golden age of
Bagdad, one of the first of the Arab writers to collect the mathematical
classics of both the East and the West, preserving them and finally
passing them on to awakening Europe. This man was Mo[h.]ammed the
Son of Moses, from Khow[=a]rezm, or, more after the manner of the

Arab, Mo[h.]ammed ibn M[=u]s[=a] al-Khow[=a]razm[=i],[8] a man
of great {5} learning and one to whom the world is much indebted for
its present knowledge of algebra[9] and of arithmetic. Of him there will
often be occasion to speak; and in the arithmetic which he wrote, and of
which Adelhard of Bath[10] (c. 1130) may have made the translation or
paraphrase,[11] he stated distinctly that the numerals were due to the
Hindus.[12] This is as plainly asserted by later Arab {6} writers, even
to the present day.[13] Indeed the phrase `ilm hind[=i], "Indian
science," is used by them for arithmetic, as also the adjective hind[=i]
alone.[14]
Probably the most striking testimony from Arabic sources is that given
by the Arabic traveler and scholar Mohammed ibn A[h.]med, Ab[=u]
'l-R[=i][h.][=a]n al-B[=i]r[=u]n[=i] (973-1048), who spent many years
in Hindustan. He wrote a large work on India,[15] one on ancient
chronology,[16] the "Book of the Ciphers," unfortunately lost, which
treated doubtless of the Hindu art of calculating, and was the author of
numerous other works. Al-B[=i]r[=u]n[=i] was a man of unusual
attainments, being versed in Arabic, Persian, Sanskrit, Hebrew, and
Syriac, as well as in astronomy, chronology, and mathematics. In his
work on India he gives detailed information concerning the language
and {7} customs of the people of that country, and states explicitly[17]
that the Hindus of his time did not use the letters of their alphabet for
numerical notation, as the Arabs did. He also states that the numeral
signs called a[.n]ka[18] had different shapes in various parts of India,
as was the case with the letters. In his Chronology