Encyclopedia of Islam

masjid

  See 

mosque

.

matam

  See h

usayniyya

.

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 c

rUsades

.

See also a

ndalUsia

; 

science

.

A. Nazir Atassi