Good questions (there are actually two of them here). Science, however, is not an 'advance'. It is just a set of falsifiable theories.
Which society? Obviously, the Western world societies, Europe, the United States, etc. Why? A pretty important cultural difference, it turns out. Our way is the Greek way. We can take apart a bit of the world, model it, twiddle with it, and use what we learn by inserting it back into the whole. That's not really easy in the integrated view of the Universe the East has. You CAN'T take a bit of the Universe apart and examine it, because you can't fill it with the inner spirit that makes that bit possible.
To be fair, some things DID come out of Eastern culture, such things as conflaguration explosive (low explosives)...rather by accident! He was actually trying to find the essence of life but wound up burning down his house. Paper also. Cranks and pistons, block printing, and even the magnetic compass came out of the Eastern culture. They used the compass as a fortune telling device. What fortunes we made on that thing when we got ahold of it and put it in our ships!
Which religion? I would say Christian being the predominant one, the religion of most of Europe and quite predominate in the United States.
That said, important theories of science came from atheists, Islam, Hindi, Buddhist, shinto, Judaism, Tao, and even believers of Norse, Roman, or Greek gods.
In the past 300 years, that would be quite definitely Christianity as the predominant religion as having created the most of the existing theories of science.
Several predominant nonscientific theories arose out of the same societies. The Theory of Abiogenesis, created in ancient Greece, and Theory of Creation, created in ancient Israel. The Theory of Evolution was also first proposed by the ancient Greeks, long before Darwin. The Theory of the Big Bang came out of Belgium from a Catholic Priest in 1931 by Georges Lemaitre. The Theory of the Continuum is much older. It's origins are unknown, but it has been discussed in ancient Greece, in ancient Israel, and in China.
All of these are not theories of science. They are just theories, and they remain circular arguments, the way they began. They are each religions.
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