That's not to belittle the contributions of actual Mohammedans (e.g. Avicenna, who really did do more than just repeat his Classical forebears), but on the whole the Islamic Golden Age was what one would expect when a supremely wealthy but weak empire (the Eastern Romans) is conquered by poor but strong barbarians: the conquerors are rich & happy for decades, living off of the wealth they have taken. Like Anglo-Saxons building their mead-halls over Roman mosaics, they enjoyed the products of a higher civilisation but were unable to match them (the Umma being rather larger than the Heptarchy, they had a much bigger base from which to decline, and a correspondingly-longer period of relative comfort).