56 3. MATHEMATICAL CULTURES II
3.2. Some Muslim mathematicians and their works. Continuing with our
list of the major writers and their works, we now survey some of the more important
ones who lived and worked under the rule of the caliphs.
Muhammed ibn Musa al-Khwarizmi. This scholar translated a number of Greek
works into Arabic but is best remembered for his Hisab al-Jabr w'al-Mugabalah
(Book of the Calculation of Restoration and Reduction). The word restoration here
(al-jabr) is the source of the modern word algebra. It refers to the operation of
keeping an equation in balance by transferring a term from one side to the opposite
side with the opposite sign. The word reduction refers to the cancellation of like
terms or factors from the two sides of an equation. The author came to be called
simply al-Khwarizmi, which may be the name of his home town (although this is
not certain); this name gave us another important term in modern mathematics,
algorithm.
The integration of intellectual interests with religious piety that we saw in
the case of the Hindus is a trait also possessed by the Muslims. Al-Khwarizmi
introduces his algebra book with a hymn of praise of Allah, then dedicates his book
to al-Mamun:
That fondness for science, by which God has distinguished the
Imam al-Mamun, the Commander of the Faithful..., that affability
and condescension which he shows to the learned, that promptitude
with which he protects and supports them in the elucidation of
obscurities and in the removal of difficulties -has encouraged me to
compose a short work on Calculating by (the rules of) Completion
and Reduction, confining it to what is easiest and most useful in
arithmetic, such as men constantly require in cases of inheritance,
legacies, partition, law-suits, and trade, and in all their dealings
with one another, or where the measuring of lands, the digging
of canals, geometrical computation, and other objects of various
sorts... My confidence rests with God, in this as in every thing,
and in Him I put my trust... May His blessing descend upon all
the prophets and heavenly messengers. [Rosen, 1831, pp. 3-4]
Thabit ibn-Qurra. The Sabian (star-worshipping) sect centered in the town of Har-
ran in what is now Turkey produced an outstanding mathematician/astronomer in
the person of Thabit ibn-Qurra (826-901). Being trilingual (besides his native Syr-
iac, he spoke Arabic and Greek), he was invited to Baghdad to study mathematics.
His mathematical and linguistic skills procured him work translating Greek trea-
tises into Arabic, including Euclid's Elements. He was a pioneer in the application
of arithmetic operations to ratios of geometric quantities, which is the essence of the
idea of a real number. The same idea occurred to Rene Descartes (1596-1650) and
was published in his famous work on analytic geometry. It is likely that Descartes
drew some inspiration from the works of the fourteenth-century Bishop of Lisieux
Nicole d'Oresme (1323-1382); Oresme, in turn, is likely to have read translations
from the Arabic. Hence it is possible that our modern concept of a real number
can be traced back to the genius of Thabit ibn-Qurra. He also wrote on mechanics,
geometry, and number theory.
