The rapid expansion of Islam took place between the time of Muhammad’s (Sallallahu Alaihi Wasallam) return to Mecca from his exile in Madina in 630 AD and the Muslim conquest of lands extending from Spain to the borders of China by 715 AD. Not long afterwards, Muslims began the acquisition of foreign learning and by the time of the Caliph al-Mansur (died 775), Indian and Persian astronomical material such as the Brahma-Sphuta-Siddhanta and the Shah’s tables had been translated into Arabic. The subsequent acquisition of Greek material was greatly advanced when the Caliph al-Ma’mun constructed a translation and research centre, The House of Wisdom, in Baghdad during his reign (813-833). Most of the translations were done from Greek and Syrian by Christian scholars but the impetus and support for this activity came from Muslim patrons.
Of Euclid’s works, The Elements, The Data, The Optics, The Phenomena, and On Divisions were translated. Of Archimedes’ works, only two – Sphere and Cylinder, and Measurements of the Circle – are known to have been translated, but these were sufficient to stimulate independent research from the 9th to 15th century.
Finally, the translation of Ptolemy’s Almagest furnished important astronomical material.
Here we will be discussing the contribution of some Muslim mathematicians who were born between the 8th and 15th centuries.
• Thabit Ibn Qurrah (836-901), a Sabian from Harran in northern Mesopotamia, was an important translator and reviser of Greek works. In addition to translating works of the major Greek mathematicians, he was a physician. He translated Nicomachus of Gerasa’s Arithmetic and discovered a beautiful rule for finding Amicable numbers, a pair of numbers such that each numbers is the sum of the set of proper divisions of the other number. The investigation of such numbers formed a continuing tradition in Islam. E.g., 17,926 and 18,416.
• Muhammad Ibn Musa al-Khwarizmi (9th century): He worked in the House of Wisdom. He introduced Indian material in his astronomical works and also wrote an early book explaining Hindu arithmetic, The Book of Addition and Subtraction to the Hindu Calculation. In another work, the Book of Restoring and Balancing, he provided a systematic introduction to Algebra, including a Theory of Quadratic Equations. Both works had important consequences for Islamic mathematics.
Hindu Calculations began a tradition of arithmetic books that by the middle of the next century led to the invention of Decimal Fractions, while Restoring and Balancing became the point of departure and model for later writers such as the Egyptian Abu Kamil. Both books were translated into Latin and Restoring and Balancing was the origin of the word Algebra, from the Arabic word for “Restoring” in its title (al-jabr). The Hindu Calculation, from a Latin form of the author’s name, Algorismi, yielded the word Algorithm.
• Omar Khayyam: He was a mathematician and poet. He discovered a general method of extracting roots of Arbitrary High Degree and his algebra contains the first complete treatment of the solution of Cubic Equations.
Omar was also part of an Islamic tradition which included Thabit and Ibn al-Haytham, of investigating Euclid’s parallel postulate. To this tradition Omar contributed the idea of a Quadrilateral with Two Congruent Sides Perpendicular to the Base, as shown in the given figure.
The parallel postulate would be proved, Omar recognised, if he could show that the remaining two angles were right angles. In this he failed, but his equation about the Quadrilateral became the standard way of discussing the parallel postulate.
Omar Khayyam constructed the Quadrilateral (shown in figure) in an effort to prove that Euclid’s Fifth Postulate, concerning parallel lines, was superfluous. He began by constructing line segments AD and BC of equal lengths perpendicular to the line segment AB. Omar recognised that he could prove that the internal angles at the top of the quadrilateral formed by connecting C and D were right angles.
Not only these few, but in the Islamic world hundreds and thousands have contributed to mathematics and it is rightly said that modern mathematics emerged from a lost Islamic library (House of Wisdom).
“The question of whose stories we tell, whose culture we privilege, and which forms of knowledge we immortalise into formal learning are inevitably influenced by the western colonial heritage.”

Mehnaz Malla