It is difficult to believe that a civilization composed of once-illiterate nomadic warriors could have a profound impact on the field of mathematics. Yet many scholars credit the Arabs with preserving much of the ancient wisdom. After conquering much of Eastern Europe and North Africa, the Islamic-based Abbasid empire moved from military conquest to intellectual enlightenment. Florian Cajori talks about this passage in A History of Mathematics. He states, “As astonishing as was the great march of conquest of the Arabs, even greater was the ease with which they put aside their former nomadic life by adopting a superior civilization and assuming sovereignty over cultivated peoples” (Cajori 99). Thanks to this cultural shift, the Abbasid Empire was able to bridge the gap between two of the most dominant civilizations in the history of mathematics; 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 had faltered as civilizations were forced to fight for survival. Islamic scholars have played a vital role in recovering the scholarly works of these civilizations and preserving them for future use. According to Carl Boyer in his book, also titled A History of Mathematics, “If it had not been for the sudden cultural awakening of Islam during the second half of the 8th century, a considerable part of ancient science and mathematics would have gone lost” ( Boyer 227). Islamic scholars have done much more than simply preserve the history of mathematics. The 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 thus creating a new field of mathematics called algeb...... half of the document... finished today. In fact, he is best known as a poet, not as a mathematician. Omar Khayyam is best known as the author of several short poems included in Edward Fitzgerald's Rubaiyat (Texas A&M). The main focus 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. An article from the Texas A&M mathematics department states: "He discovered exactly what must be shown to prove the parallel postulate, and it was on these ideas that non-Euclidean geometry was discovered" (Texas A&M). In short, the Euclidean parallel postulate is: 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 consolidated this idea by using a quadrilateral to show the existence of parallel lines.