Bede the Venerable Blogger (not to be confused with the Venerable Bede) has made somewhat of a specialty of examining the progress of science in the Middle Ages, particularly noting that science flourished in Christian lands, and that Christianity's view of an orderly and stable creation was among Christianity's helpful contributions to the rise of science. I suppose it's easier to develop science when believing the world is orderly and stable, as opposed to believing it is an illusion, or is subject to capricious whims. But I think a few more things can be added to the list of things Christianity has contributed towards the rise of science, namely: the encouragement of a creative imagination and the benevolent or loving direction of human endeavor.
The field of theoretical science does not advance in large steps solely by collecting or processing data. The earliest steps of the scientific process -- theorizing, speculating, hypothesizing -- are the ground of the human imagination. In the case of theory, we try to form a model in our mind of what is true. When reality proves to be different from previous concepts, forming a new working model requires a substantial amount of imaginative thinking. The scientific method does not generate new thoughts or models, but asks that these be brought to it from the outside as a starting point for testing. The formation of a hypothesis or the steady building of a theory depends on the imagination. Science, as naturalistic and observational methodology, is not capable of the intuitive leaps that its development has depended on for its reputation.
The field of applied science -- that is, technology -- is even more indebted to the creative imagination. The body of knowledge accumulated by science can make some small advances with simple observation, even in a complete absence of imaginative new theories. But the application of science to the real world is a different matter. Without imagination there would be no inventions. While some naturalists have been quick to claim all of technology as the realm of pure naturalism, still technological advances depend heavily on the creative and imaginative aspects of humanity, and on a choice of how to apply the advances made. Science, as a method, is not capable of desiring to be good and beneficial to people, despite that is one of its major boasts. Science, in isolation, pursues knowledge and is not particular about its uses. The benevolent, useful applications that have made science a blessing more often than a curse owe themselves to people applying themselves with their own personal or cultural, religious-steeped agendas of being blessings to other people, to act in love and service for humanity rather than for power or self-gratification.
Christian culture has taken criticism from various fronts for its love of imagination and fantasy. Christianity, however, sees the imaginative and creative spirit as part of humanity's role in creation, part of the image of God. To be creative, it is necessary to first imagine what you create. The Christian lands first excelled in imagination, which in turn led to the more outwardly noticeable excellences not only in visual art, drama, and music, but also in science and technology. Without imagination, there would have been no airplane, no telephone, no radio, no television, no lightbulb. Without imagination there would have been few advances in medicine or in mechanical and electrical technology.
Without "moral imagination" -- I wonder if it would be close to say "without pondering how to act on love" -- would the human mind direct itself to benevolent ends?
Certain outspoken scientists have decried religion for its supposed separation from reality. But it is only a certain separation from our current reality that allows any progress to be made towards another reality. The Christian embrace of the vision of paradise -- and of the potential for paradise within creation -- is one thing that enables progress towards something more closely resembling paradise. Christ's teaching of the primacy of love has given us the direction that drives us to find technologies that are widely, benevolently useful. Without imagination and love, science has no method of achieving progress and no reason to pursue benevolent advances that are a blessing to the world as a whole.
If naturalists wish a steady supply of creative minds that find useful rather than selfish applications for our knowledge, it would be worthwhile to consider the extent to which creative minds are generated through a culture that is fertile ground for imagination, is well-directed towards paradise, and expresses itself benevolently in love. It would be worthwhile to recognize the debt to religion in creating minds of a certain outlook and habit, and cultures that embrace imagination, creativity, benevolence, and progress towards paradise. If naturalism completely overtakes culture with a reductionist point of view, it will find it has reduced the reserves of cultural creativity needed for science to hypothesize, theorize, and flourish. In an excessively naturalistic culture, science may find itself with a shortage of creative minds directed towards useful pursuits.
I do not consider this to be an argument for Christianity's mere usefulness as much as for Christianity's firmer grasp of reality -- ultimate reality -- towards which progress can be made, however imperfectly.
Note on religions in general: Parallel arguments can be made on some level for any benevolent teaching and any paradise-oriented teaching to provide a fertile cultural background for science and technology. In this respect, most religions have some teaching of benevolence, though Christianity has a far stronger emphasis on the primacy of love than the other religions, emphasizing benevolent actions even above self-improvement, self-actualization, self-purification, or a goal of pursuing one's own personal enlightenment. Christiantiy sees those other things as only attainable through the pursuit of love, not as things attainable in themselves. Likewise, a number of other religions have some recognition of paradise, though Christianity has a far stronger teaching and vision of paradise than many other religions which acknowledge some form of paradise. More could also be said of Christianity's insistence that all poor people deserve compassion and help (it is never the fact that they were evil in a previous life that makes them somehow deserve a lower status in this life) and that sickness is best viewed as an occasion for compassion rather than a judgment from God. Christ's own actions were driven by love and focused on healing, feeding, teaching, forgiving, restoring dignity, restoring love, and restoring peace; therefore Christ's followers see these as the main aims of useful human action.