I've been asked, by someone who's unfamiliar with my tendency to run off at the keyboard, to discuss the links between science and mathematics, on the one hand, and religion and imagination, on the other. Since that's not something that lends itself to soundbites, I'm going to start here, rather than Twitter. I have trouble saying ANYTHING in 140 letters. I'm afraid I'm also going to pass on the mathematics. I'm allergic to it. ( Like Gerard, I don't even know what a cosine is. )
The Middle Ages saw a tremendous flowering of scientific discovery. Unfortunately, that's been pretty much forgotten. The scientific method itself has its roots in the medieval world. Just look at this outline on Wikipedia, which is surprisingly good. Have a look. I'd be here all night if I even tried to start a list. Medieval science formed the foundation necessary for later development in almost every discipline. How was that possible if, in an "age of faith", religion opposed scientific inquiry every step of the way? Simple. Religion didn't impede progress. It enouraged progress.
But what about the dreaded Inquisition? Witch burnings? Well, for the most part, all that came much later. For most of the Middle Ages, scholars could study and discuss without having to watch over their shoulders. Remember, the university was a medieval invention. As long as people steered clear of a few hot-button topics, they could pretty much do as they pleased.
I'm going to offer two reasons why I believe religion aided in the development of science.
The first, though I'm talking about Catholic Europe, can be applied with equal validity to medieval Islam, and, though to a lesser extent, to medieval China and to the later Protestant countries of Northern Europe. Science thrives best in a stable cultural environment that, within a framework of agreed-upon beliefs, encourages inquiry and is open to the exchange of information. Religion, when its position isn't being threatened by internal or external forces, can form the bedrock of such an environment. ( Of course, when threatened, all bets are off. ) Through belief in a Creator, it gives cause to believe that the creation operates under some form of rational order. This belief encourages inquiry into how and why that order is formed
My second reason is specific to Catholicism, but I suspect it could apply to medieval Islam, as well. ( I'm not qualified to do more than speculate on that. )
Catholicism, at its best, presents the world as created by God, but operating and developing under rational and identifiable laws. Yet, at the same time, Catholicism, again at its best, presents the world as something infinitely beautiful and miraculous. In my opinion, it's that two-pronged approach; that ability to see nature as a multifaceted gem; that encouraged medieval scholars to try to learn as much as possible about the hows and whys of divine order, and, in the process, lay the groundwork for methods and disciplines that survived the waning of the "age of faith". To me, that blending of practicality and poetry, of reason and mysticism, is the true genius of the medieval world, and in it we might be able to find lessons for our own post-modern world, which longs for just such a blend.