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 of Ancient Nations_ he gives the sum of a
geometric progression and shows how, in order to avoid any possibility of
error, the number may be expressed in three different systems: with Indian
symbols, in sexagesimal notation, and by an alphabet system w