It is hard to believe that a civilization composed of formerly illiterate nomadic warriors could have a profound impact on the field of mathematics. Yet many scholars credit the Arabs with preserving much ancient wisdom. After conquering much of Eastern Europe and North Africa, the Islamic Abbasid Empire moved from military conquest to intellectual enlightenment. Florian Cajori talks about this transition in A History of Mathematics. He states: “As astonishing as the great march of conquest of the Arabs was, the ease with which they cast aside their ancient nomadic life, adopted a higher civilization and assumed sovereignty over cultivated peoples” (Cajori 99) was even more surprising. Through this cultural shift, the Abbasid Empire was able to bridge the gap between two of the most dominant civilizations in mathematical history; the Greeks and the Italians. By the time of Islamic expansion, much of the world had fallen into massive intellectual decline. The quest for knowledge failed as civilizations were forced to fight for survival. Islamic scholars played a vital role in recovering the scientific works of these civilizations and preserving them for future use. According to Carl Boyer in his book, also titled A History of Mathematics, "without the sudden cultural awakening of Islam during the second half of the 8th century, much more ancient science and mathematics would have been lost." ( Boyer 227). Islamic scholars did more than just preserve mathematical history. Persian mathematicians, Abu Ja'far Muhammad ibn Musa Al-Khwarizmi, Abu Bakr al-Karaji and Omar Khayyam, attached rules and provided logical proofs to Greek geometry, creating a new mathematical field called algebra.... .. middle of paper ......h is finished today. In fact, he is best known as a poet and not as a mathematician. Omar Khayyam is best known as the author of a few short poems included in Rubaiyat by Edward Fitzgerald (Texas A&M). The main emphasis here will be on his geometric proofs concerning the root of third degree polynomials; however, he also pushed for the use of rational numbers and helped prove the parallel postulate. A paper from the Texas A&M mathematics department states: "He discovered exactly what needed to be demonstrated to prove the parallel postulate, and it was on the basis of these ideas that non-Euclidean geometry was discovered" (Texas A&M) . In short, the Euclidean postulate of parallel is as follows: given a point and a line, there can only be one line that passes through the point and is parallel to the given line. (See figure below) Khayyam solidified this idea by using a quadrilateral to show the existence of parallel lines.