1. Aristotle
Science is Aristotle's method. Later, Aristole's method would create conclusions which conflicted with some of Aristotle's conclusions. After Aristotle's substantive errors were cleared out the Renaissance and Enlightenment flared, in a SPACE created by:
2. Jesus.
In the Christian West, Jesus' words inserted a SPACE between the state and religion.
This space was only a potential spce until Constantine, then for 1000 years Christendom fought over this space, which took on an intellectual life of its own by the year 1100, whether the individual thinker believed in Jesus' words or not.
The separation of church and state is an implication of Jesus' attitude to the state in the NT.
Islam lacks the words of Jesus. Hence, there is no space between secular power and real or imagined religious truth.
In Islam, the natural tendency of religions to demand compliance with their worldview choked off Aristotle when his method began to produce conclusions at odds with Islam.
In Christendom, there was a great struggle, but the Jesus space survived and expanded to allow the Aristotelian explosion of knowledge in the Modern West.
So it was Aristotle's brain plus Jesus' attitude toward coercion.
"Oh, he may have been wrong about the doctrines but he was right about the method". No, he wasn't. He thought demonstration (logic) covered more than it actually does. He thought speculation was out of place in matters that "should be" deductive - when actually science has to just plain guess and see what works by trial and error. "OK, so he didn't know the method yet but he was right about empiricism". No, he wasn't an empiricist. He taught that strictly speaking there was no scientific knowledge about anything that could change, including all perceptables. Aristotle is not the definition of human reason.
But in the high middle ages, lots of people thought he was. They thought so in part because that position was defended by people like Averroes, his ablest commentator and the one who transmitted a recovered Aristotle to the west. Averroes was in an argument with intellectual theologians of medieval Islam, before their descent into literalism.
Those theologians defended the claims of revelation against reason using the weapon of skepticism. Against them, Averroes used Aristotle as a dogmatist, as an optimist about the power of logic to achieve certain demonstrations. He presented things as though reason were based on logic and could not be doubted, while theology was speculative and debatable, producing only confusion and division as a result.
The propositions that he was defending as though they were demonstrated truths were things like the non-existence of any vaccum, the continuity of matter and falsehood of the hypothesis of atoms, the existence of a fifth element in the region above the moon, the eternity of the visible, physical world, Aristotlean physics, the earth at the center of the heavens, and certain human knowledge of unvarying natural necessities. His opponents taught against these the weakness of human reason, the existence of atoms moving in void, the temporal creation of the world, the uncertainty of all human knowledge outside logic and pure mathematics.
Nobody today, thinking of the results of modern science on the one hand and what Galileo rebelled against on the other hand, would recognize the latter position as the theological one. But so it was, in Islam. The Asharites were not defenders of human reason. But their actual estimate of its abilities was closer to Hume and Popper than Averroes' views were. Averroes thought he was defending human reason. But Galileo was persecuted for disagreeing with essentially his understanding of human reason and its supposed results, transmitted to the west via Acquinas.
The whole tale cannot be understood as a morality play in which the truth was already the secure possession of one side or another at every stage, with white hatted defenders of that truth beset by persecuting ignorant black hats who had to be pig-headed not to know better. The sober reality is that none of the parties to these disputes was right. They all made different errors. None was in possession of the truth. Not in actual doctrine, not in method, not in proper assessment of the actual abilities and limitations of human reason.
And not because there is no truth in these matters or it all depends on somebody's point of view or as children of their times etc. No, just plain wrong, about matters where it is possible to be right. People you might want to think are on the right side are making arguments that are insupportable. They are losing arguments justly, sometimes against people who are worse than they are. The individual human mind is weak - even the strongest human minds. Thought depends on advances previously made and on repeated correction of error. And those will always be in tension with each other. They have to be - it is precisely that tension that stresses doctrines and exposes errors.
As for space and Constantine, um, it was with Constantine that Christianity was first used as a buttress of absolute monarchy. Read Acton's "History of freedom in Christianity" sometime. It is a much more convoluted story than you present. No, doctrines of plentitude of power and indexes of forbidden books did not create the space that made possible modern science. Nor rival doctrines of literalism. The most one might say is that violent struggles between principles hostile to liberty and free inquiry, sometimes created a space between less hostile to those things. And that many movements at various times made appeals to such principles to combat persecution, where and while they were weak.