Jaroslav Pelikan, “The Heroine of the Qur’an and the
Black Madonna.” In Mary through the Centuries: Her
Place in the History of Culture (New Haven, Conn.:
Yale University Press, 1996); Aliah Schleifer, Mary
the Blessed Virgin of Islam (Louisville, Ky.: Fons Vitae,
1998); Jane I. Smith and Yvonne Y. Haddad, “The Virgin
Mary in Islamic Tradition and Commentary.” Moslem
World 79:3–4 (July–October 1989): 161–187; Barbara F.
Stowasser, Women in the Qur’an, Traditions and Interpre-
tation (New York: Oxford University Press, 1994); W.
M. Thackston, trans. The Tales of the Prophets of al-Kisa’i
(Boston: Twayne Publishers, 1978).
masjid See mosque.
matam See husayniyya.
mathematics
Mathematics occupied a prominent place on
the scientific scene in the Arabo-Islamic empire.
Although all works were translated into or written
in Arabic, all ethnic and religious communities of
the empire produced scholars who contributed to
mathematics. The Arabo-Islamic scholars digested,
commented on, summarized, and then built upon
their predecessors’ works regardless of their reli-
gion or ethnicity; their contributions to mathemat-
ics, regardless of its nature or size, were absolutely
crucial for any further developments in the field.
Translation of other works received its biggest
thrust under the patronage of the Abbasid caliph
al-Mamun (r. 813–833). Mathematical works were
translated from sources such as Greek/Hellenistic,
Persian, and Indian. A list of translators, trans-
lated books, and scholars was produced by Ibn
al-Nadim (10th century) in his encyclopedic book
al-Fihrist.
In the field of arithmetic, the Arabo-Islamic
scholars identified Indian arithmetic as the most
efficient, from which they borrowed and perfected
Indian numerals, the decimal system, the place-
value and the ideas of zero, fractions, root extrac-
tions, and associated operations. Later on, they
integrated received and translated knowledge into
a coherent body, which was then subject to further
refinement.
The field of algebra was inaugurated by the
work of al-Khawarizmi (ninth century). He
introduced a complete terminology for solving
arithmetical and geometrical problems through
radicals, the idea of the unknown, the idea of
equations, the first and second-degree equa-
tions, algorithmic solutions, and the demonstra-
tion of the solution formula. He actually gave
his name to all systematic and step-by-step
methods of solving problems, namely, the algo-
rithms. Thabit ibn Qurra (d. 901) later gave
a geometrical explanation of the equations of
al-Khawarizmi. However, it was al-Khayyam (d.
1123) who elaborated a geometrical theory for
equations of degree equal to or less than three. A
full treatment of the solution of cubic equations
was given two generations later by Nasiral-Din
al-Tusi (d. 1274).
The Arabo-Islamic scholars added original
contributions in all areas of the great Greek
geometrical tradition, including laying the foun-
dations of geometry, geometric constructions,
geometric transformations, and projections.
In addition, they established the connection
between geometry and algebra. Finally, in trigo-
nometry they devised trigonometric formulae
for a triangle (these formulae were originally
given for a sphere), and they defined and intro-
duced the tangent function. These contributions
found applications in astronomy, engineering,
optics and mUsic. Many of the works of the
Arabo-Islamic mathematicians were translated
into Latin after they entered Europe through
trading contacts with Byzantium, Spain, and
Sicily, and through interactions occasioned by
the crUsades.
See also andalUsia; science.
A. Nazir Atassimathematics 461 J