@goldenfinger It was the Byzantines would first recovered it, but it was the Islamic Empire that really took it, improved it and remodeled it. I probably could've made that more clear.
@fasces well I do understand your point, as the Islamic Empire is often neglected in school systems in basic history (at least here in Canada; I was blessed with taking advanced stuff), then I figured I should give a brief rundown of their accomplishments. As for why I think they were the greatest, is in fact, based on these achievements. To me, the issue of "best" boils down to the empire that not only expanded their influence over a large area, but did so not only through conquest, but through trade and a general embracing of their culture. This is not to say that the British and Mongols did not do this, and in fact, I am not so sure that the Muslim did this better. My whole point in bringing them up was to add their name to the discussion (also I find the Islamic world to be vastly more interesting then that of Europe). The Muslim were able to rise from humble beginnings, much like the Mongols and Romans, and grow from a formidable regional power to a world power. Although there is no doubt that Islam was spread by the sword, their merchants were some of the greatest of all time. And their desire to learn and embrace new culture is unparalleled. Look at the example of Ibn Battuta: a great Muslim scholar who traveled the world, seeking out new knowledge to expand that of the empire as a whole. Also, as people saw the wealth and equality of the Muslims, they would often join without the need on conflict. Muslims could be found far outside the borders of the formal empire (like Mali).
And as this expansion was taking place, internally, scholars and mathematicians were making amazing leaps forward (Arabic numerals), and medicine was being developed at an incredibly more efficient rate. As well, as the Islamic Empire came to dominant that part of the world, Arabic became the central language in trade; a role it wouldnt fully loss until the 19th century. Say what you want, but those are certainly the characteristics of greatness, if ever I saw them