Rome succumbed to barbarian impertinence and classical civilization died off. Good riddance; while it accomplished many great things, the economic foundation of the system was slavery. Fortunately, Mohammed arrived on the scene in the nick of time. Arab armies overran Mesopotamia and the southern littoral of the Mediterranean and built a great empire that was fundamentally more humane and civilized than Roman civilization ever was. The glory of Arab civilization lay in three great principles: tolerance, military power, and literacy.
The Arabs built the first great civilization that rejected racial or ethnic discrimination. Roman civilization had always maintained strict hierarchies based on family heritage and citizenship, but the Arabs embraced anybody who accepted Islam as a full member of their civilization. Within two generations of conquering Egypt, they had completely assimilated that huge population into their system. Moreover, they tolerated other religions: Jews and Christians had to pay higher taxes, but otherwise were free to practice their religions unhassled.
Militarily, the Arab innovation was the creation of mass armies of truly motivated soldiers. The Roman system was built on soldiers motivated not by patriotism or religious fervor but by economic necessity. Such armies, disciplined by a strong class of NCOs (the centurions) and a long tradition of victory, functioned well in the great days of Roman power, but as the legacy of greatness eroded, these armies lost their fighting spirit. The Arab soldiers, by contrast, were fired with religious enthusiasm. They believed in their mission and fought with vigor. Despite poor discipline (and some rather poor generals), this rabble of determined warriors swept away the soldiers of the old order and conquered everything before them. Moreover, since they fought for an idea rather than pillage and spoils, they did not inspire the same determined opposition that previous armies had faced. The Arab conquests were not accompanied by the destruction that marked all previous warfare. They weren’t coming to kill and loot; they just wanted to expand the empire of Allah. Their rulers might have wanted to duke it out to the death, but the people whose lives they intended to sacrifice to remain in power didn’t go along with the deal. Resistance crumbled before the advancing wave of enlightened Arab power.
The third foundation of Arab greatness was mass literacy. The Koran was the book of truth, and every single Moslem was expected to learn and understand it. I doubt that literacy rates in the early Arab Empire ever exceeded even 30%, but even so this was far higher than what had been achieved in classical civilization. Where the Mesopotamian and Egyptian civilizations had literacy rates way below 1%, Greek civilization pushed that literacy rate above some magic threshold. It was rather like what we now call "network effects". The value of email increases as some power function of the number of people with email addresses. If only 1% of your friends and associates have email capacity, then email isn’t very useful, but above some critical threshold (30%? 50%?), email becomes immensely useful. Above this threshold, so many people are talking to so many other people that a kind of group deliberation synergy emerges; ideas flow faster, are trimmed and polished more quickly. That’s what literacy did to Greek civilization. Roman civilization had more absolute literacy but the overall literacy rate was lower than in Greek civilization, which is why the Romans did not maintain the intellectual momentum of the Greeks. The Arabs achieved a literacy rate comparable to the Greek rate, but extended over a much larger group of people. The result was another, albeit smaller, explosion of human thought.
Most Westerners, schooled in the ethnocentric traditions of Western schools, fail to appreciate the Glory that was Islam. (By the way, the transition for "Arab Empire" to "Islamic Empire" was quick because the Arabs were so tolerant; after they conquered everybody in sight, they made them full partners, and within a few generations the Arabs were no longer the dominant ethnic group in most Islamic countries. This never bothered them because they didn’t keep score that way.) But the Islamic cultural achievement was every bit the equal of the Greek achievement. Of course, they didn’t concentrate on the same things the Greeks did. Since they didn’t like representations of the human body, sculpture and painting were ignored. But poetry, music, architecture, mathematics, astronomy, chemistry, and geography flowered. We Westerners cannot appreciate the beauty of Arabic poetry and music, but those few who have mastered the language swoon with delight in describing the delicate beauty of their verse. More certifiable are their achievements in architecture. Arab architects disdained the Greek columns as bulky; they strove for lighter, airier designs, and they found their vehicle in the Roman dome. The Romans deserve credit for inventing this three-dimensional extension of the arch, but the Arabs transformed it from the stolid to the celestial.
My training as a scientist affects my values; Islamic achievements in mathematics and science impress me the most. Here they went way beyond the Greeks. Where the Greeks had concentrated on geometry, the Arabs invented algebra. Where the Egyptians had developed methodologies for calculation that fell just short of my definition of algebra, and the Greeks had broken the first ground in this field, the Arabs ploughed it and made it fertile. The definitive work, written by Muhammed ibn Musa, also known as al-Khwarizmi, introduced the Arabic term "al-jabr" to the European world, which mispronounced it as "algebra". Al-Khwarizmi himself was the source of our word "algorithm". Western civilization did not catch up with Arabic mathematics and science for eight hundred years.
Ironically, the same religion that powered Islamic civilization later acted as a brake on it. Islamic thinkers, exploring ever-wider realms of thought, soon began to ask questions that made religious zealots uncomfortable. They reacted to this threat with book-burnings and executions. After its initial explosion in the eight, ninth, and tenth centuries, Islamic thought grew conservative, tentative, and staid. Some of the works of the great Islamic thinkers were lost forever; others simply slipped into obscurity. The flame of Reason, ignited by the Greeks, maintained by the Romans, and advanced by the Arabs, might have sputtered out, but for the efforts of a few enlightened Europeans. For by 1100 AD, Europe was ready to pick up the ball that the Arabs were now fumbling.