Mathematics in medieval Islam
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, is the mathematics developed in the Islamic world between 622 and 1600, during what is known as the Islamic Golden Age, in that part of the world where Islam was the dominant religion. Islamic science and mathematics flourished under the Islamic caliphate (also known as the Islamic Empire) established across the Middle East, Central Asia, North Africa, Southern Italy, the Iberian Peninsula, and, at its peak, parts of France and India as well. Islamic activity in mathematics was largely centered around modern-day Iraq and Persia, but at its greatest extent stretched from North Africa and Spain in the west to India in the east. While most scientists in this period were Muslims and wrote in Arabic, many of the best known contributors were Persians  as well as Arabs, in addition to Berber, Moorish and Turkic contributors, as well as some from other religions (Christians, Jews, Sabians, Zoroastrians, and the irreligious). Arabic was the dominant language—much like Latin in Medieval Europe, Arabic was the written lingua franca of most scholars throughout the Islamic world.
Use of the term "Islam"
Bernard Lewis writes the following on the historical usage of the term "Islam" in What Went Wrong? Western Impact and Middle Eastern Response: "There have been many civilizations in human history, almost all of which were local, in the sense that they were defined by a region and an ethnic group. This applied to all the ancient civilizations of the Middle East—Egypt, Babylon, Persia; to the great civilizations of Asia—India, China; and to the civilizations of Pre-Columbian America. There are two exceptions: Christendom and Islam. These are two civilizations defined by religion, in which religion is the primary defining force, not, as in India or China, a secondary aspect among others of an essentially regional and ethnically defined civilization. Here, again, another word of explanation is necessary." "In English we use the word “Islam” with two distinct meanings, and the distinction is often blurred and lost and gives rise to considerable confusion. In the one sense, Islam is the counterpart of Christianity; that is to say, a religion in the strict sense of the word: a system of belief and worship. In the other sense, Islam is the counterpart of Christendom; that is to say, a civilization shaped and defined by a religion, but containing many elements apart from and even hostile to that religion, yet arising within that civilization." In this article, "Islam" and the adjective "Islamic" is used in the meaning described above; that is, of a civilization.
Origins and influences
The first century of the Islamic Arab Empire saw almost no scientific or mathematical achievements, since the Arabs, with their newly conquered empire, had not yet gained any intellectual drive and research in other parts of the world had faded. In the second half of the 8th century Islam had a cultural awakening, and research in mathematics and the sciences increased. The Muslim Abbasid caliph al-Mamun (809–833) is said to have had a dream where Aristotle appeared to him, and as a consequence al-Mamun ordered that Arabic translation be made of as many Greek works as possible, including Ptolemy's Almagest and Euclid's Elements. Greek works would be given to the Muslims by the Byzantine Empire in exchange for treaties, as the two empires held an uneasy peace. Many of these Greek works were translated by Thabit ibn Qurra (826–901), who translated books written by Euclid, Archimedes, Apollonius, Ptolemy, and Eutocius. Historians are in debt to many Islamic translators, for it is through their work that many ancient Greek texts have survived only through Arabic translations. Greek, Indian and Babylonian all played an important role in the...