54 3. MATHEMATICAL CULTURES II
(in European languages) mathematical work comparable to what was being done in
Europe at the same period, and a few European scholars were already reading these
journals to see what advances were being made by the Japanese. In the twentieth
century the number of Japanese works being read in the West multiplied, and
Japanese mathematicians such as Goro Shimura (b. 1930), Shoshichi Kobayashi (b.
1932), and many others have been represented among the leaders in nearly every
field of mathematics.
3. The Muslims
From the end of the eighth century through the period referred to as Medieval in
European history, the Umayyad and Abbasid Caliphates, centered in what is now
Spain and Iraq respectively, produced an artistically and scientifically advanced
culture, with works on mathematics, physics, chemistry, and medicine written in
Arabic, the common language of scholars throughout the Muslim world. Persian,
Hebrew, and other languages were also used by scholars working in this predomi-
nantly Muslim culture. Hence the label "Islamic mathematics" that we prefer to
use is only a rough description of the material we shall be discussing. It is conve-
nient, like the label "Greek mathematics" used above to refer to works written in
the culture where scholars mostly wrote in Greek.
3.1. Islamic science in general. The religion of Islam calls for prayers facing
Mecca at specified times of the day. That alone would be sufficient motive for
studying astronomy and geography. Since the Muslim calendar is lunar rather than
lunisolar, religious feasts and fasts are easy to keep track of. Since Islam forbids
representation of the human form in paintings, mosques are always decorated with
abstract geometric patterns (see Ozdural, 2000). The study of this ornamental
geometry has interesting connections with the theory of transformation groups.
Hindu influences. According to Colebrooke {1817, pp. Ixiv-lxv), in the year 773 CE,
al-Mansur, the second caliph of the Abbasid dynasty, who ruled from 754 to 775,
received at his court a Hindu scholar bearing a book on astronomy referred to in
Arabic as Sind-hind (most likely, Siddhanta). Al-Mansur had this book translated
into Arabic. No copies survive, but the book seems to have been the Brahmas-
phutasiddhanta mentioned above. This book was used for some decades, and an
abridgement was made in the early ninth century, during the reign of al-Mamun
(caliph from 813 to 833), by Muhammed ibn Musa al-Khwarizmi (ca. 780-850),
who also wrote his own treatise on astronomy based on the Hindu work and the
work of Ptolemy. Al-Mamun founded a "House of Wisdom" in Baghdad, the capital
of his empire. This institution was much like the Library at Alexandria, a place of
scholarship analogous to a modern research institute.
In the early days of this scientific culture, one of the main concerns of the schol-
ars was to find and translate into Arabic as many scientific works as possible. The
effort made by Islamic rulers, administrators, and merchants to acquire and trans-
late Hindu and Hellenistic texts was prodigious. The works had first to be located,
a job requiring much travel and expense. Next, they needed to be understood and
adequately translated; that work required a great deal of labor and time, often
involving many people. The world is much indebted to the scholars who undertook
this work, for two reasons. First, some of the original works have been lost, and
