***Not to sound like Jisbond, but if it weren't for Islam, there would have been nothing for Christianity to build off of after they exited the dark ages!***
Islam deserves credit in accelerating the science of Europe, but it was only an acceleration. The early university in Europe predated the Crusades which is where much of the exposure to the Greek philosophers (e.g., Aristotle) occurred. Had Islam never invaded Spain and Italy, it is likely that Europe would have exited the 'dark ages' with the growth of universities as well as the growth of city-states which encouraged independence from the Papacy in Rome. Maybe a couple of more centuries would have been needed, but contrary to popular view, the 'dark ages' were not all that dark in the area of technology. A number of changes occurred after the Barbarian tribes sacked Rome and started to settle into empires.
***As for Asia, India hasn't progressed much because of problems coming directly from British occupation. China has a well established science core, as does the remaining of the Far East.***
True, however keep in mind that Europe had a quest for 'truth' as well as publicizing that truth (evangelicalism) which I think came from Christianity. I think, this is a core necessity of scientific progress. Also, early science developed from natural philosophy. Christianity more or less encouraged philosophy because it was seen as many as way to evangelize the Gospel to the unconverted. Also, the development of Protestantism encouraged the laymen to become involved in doctrines, which might explain why universities became larger and encouraging average citizens to become educated. This is one of the many keys that brought more minds into scientific discussions.
It is difficult to agree what role these attributes of Christianity played in the development of science, but in my mind these attributes were absolutely necessary. Again, I don't think it is a coincidence that science developed in Christian Europe.
Warm regards, Harv