We are interested in Islam insofar as it has preserved and handed down the traditions of Greek mathematics. A little background is necessary.
Spelling: Since the Arabic alphabet is different from the English alphabet, there are often several spellings used for one and the same Arabic word. Islam is the faith of those who believe in the prophet Muhammad, also spelled Mohammed or Mahomet. This faith is also called Mohammedanism, or Muhammadanism, or Mahometanism. The followers of the faith are called Islamic, Muslim, Moslem, Muslem, or Moslim. The American Heritage Dictionary (1973) notes, "Moslem is the form predominantly preferred in journalism and popular usage. Muslim is preferred by scholars and by English-speaking adherents of Islam." (855)
The Arabian peninsula remained unconquered both by Alexander and by the Roman and Byzantine Empires. In the city of Mecca, in the late 6th Century, the prophet Muhammad was born, to whom the angel Gabriel dictated the Koran, the holy book of Islam. According to Lindberg, "Muhammad both praticed and taught the necessity of holy war and compulsory conversion." Muhammad died in 632, having subjugated the entire Arabian peninsula. In a century, all of Alexander's Asian and North African conquests were taken along with northwestern Africa to Morocco and across the straits of Gibraltar to Spain. (166)
Scholars argue over the degree to which Greek science was known, studied and taught in the Islamic Empire. Lindberg describes two camps: those who support the "marginality thesis," which asserts that Greek writing never made a deep impression on Islamic culture but survived in the margins of Islamic academies, studied by a few great scholars; and those who support the "appropriation thesis," which asserts that Greek science was valued for its utility and therefore was more widely known and understood. Lindberg states that "Islamic education did nothing to prohibit the foreign sciences; but neither did it do much to support them." (173-175)
Lindberg gives his version of the intellectual climate of Arabia:
Muslims themselves divided learning into two categories: traditional on the one hand; foreign or rational on the other. The traditional disciplines were those based on the Koran: grammar, poetry, history, theology, and law. These rested on divine authority and were aften taught orally (reflecting the oral nature of Muhammad's revelations and his own teaching); the obligation of the practitioner of such disciplines was completeness and fidelity of transmission. By contrast, the foreign disciplines obtained from the Greeks were of human rather than divine origin; they were apprehended by reason, rather than accepted on the basis of authority or tradition; their transmission was primarily by means of written word, and they were subject to critical commentary and correction. (173)