I am writing a research paper on the interplay between science and religion, and need some examples of times when religion has benefited or inspired science and technology.
Geology -- the science of Geology was basically invented by the search for proof of the world-wide Noah's Flood as depicted in the book of Genesis chapter 6+.
This search by both religious (Christian) churchmen and laymen who had interests in science used their emergent knowledge of rocks, strata, and other features common to Geologic structures and artifacts to find evidence that there was a world-wide flood. They believed that the earth would show evidence of flood geology.
During this process which took decades and was passed down from one generation of "flood scientists" to the next started to discover not only evidence of new geologic science but indications that the Earth was much older than they first thought and also that evidence proving a world-wide flood could not be found.
As a result of their work and the work of others in parallel discovery, the science of geology was born and matured to a point that it was totally separate from its early Flood Geology roots.
This entire story is told in a very excellent way by a book, "The Rocks Don't Lie -- A Geologist Investigates Noah's Flood" by David R. Montgomery, Professor of Earth and Space Sciences at University of Washington (Seattle). I highly recommend the book.
I would like to point out that this is not an Anti-Christianity book nor does it use this history to defame Christianity. It is a fair and balanced story of the history of the birth of Geology in this hunt for Noah's Flood.
There is a line of thought that says the reforms of John Calvin and other Protestant leaders lead to a change in the idea of "work", which in turn made the Industrial Revolution possible.
There are many works expounding this hypothesis. Here is one I found by googling...
Prior to Calvin, work was not considered a good thing. It was something the lower classes did. Anyone who was anyone didn’t do physical work. They lived lives of leisure and contemplation. They devoted themselves to music and poetry and literature and art. Such was their "higher calling." The lower classes did not aspire to much beyond their laborious lower class callings. That is something of a simplification, but it is, in a nutshell, the way it was.
Calvin and the other Protestant Reformers of 16th century Europe challenged all that. They postulated that work, physical work, was good, that God created man to work, that all men, regardless of their position in society, were called to work, that there was dignity in work, and that work was a form of worship. This teaching is best summed up in the term “Protestant work ethic.” It started with the Reformation Protesters. It started with John Calvin. LINK
During the "dark ages" science was kept alive essentially in monasteries. Benedictine and Cistecians studied and catalogued properties of soils and resulting wines.
The Royal Society, founded in 1662, perhaps the first scientific society ... the majority of the founding members were Puritans.
Not bound by tradition, Puritan schools fostered science. Theodore Haak, a professor at the largely Puritan Gresham College, initiated the meetings of the "invisibles." Other Protestant schools revolutionized medicine about the same time, and it was a Protestant school which later trained John Dalton, author of modern atomic theory. LINK