What we call science, or, more properly, natural science, has been around at least since Aristotle started organizing categories of animals and thereby founded biology.
But science was re-started, and what we call modern science arose and found its home in Europe during the late Middle Ages and Early Modern Era. Astronomy, physics, chemistry, biology, and the mathematical infrastructure needed to form them constituted a new era in scientific thinking, an era which continues to this day. But why did this happen in Europe, and not somewhere else in the world?
European culture in the late Middle Ages had reached a point, after several centuries, at which it could clearly formulate six ideas which contributed to a scientific mindset:
 The physical world is real, not an illusion. Many non-European cultures had embraced a philosophy which taught that the physical world is an illusion. Eurpean philosophers taught that the world is real and can be known. This assumption primed Western thinkers to value the physical world and to consider it worthy of study.
 Nature is good but not divine. Many primitive cultures held animistic beliefs, which taught that the world is the home of the divine or an emanation of God's own essence. Consequently, they believe that nature is alive with sun gods, river goddesses, and astral deities. Eurpean philosophers taught that the sun and the moon are not gods; historians call this the "de-deification" of nature; nature is not to be worshipped, it is to be studied.
 Nature is orderly and predictable. Another unique contribution of European thought was the ideas of the laws of nature. Nobody had ever before used the word "law" in relation to nature. Many other cultures had regarded nature as mysterious, dangerous, and chaotic. Early scientists acted on the belief that nature is orderly, before they had amassed enough evidence to prove it. Modern physics is based on the ideas that the universe is rational because it is understandable, uniform because law like gravity operate in the same way on different planets, and organized according to the laws of mathematics.
 Humans can discover nature's order. Early scientists acted on the hypothesis that the order in nature can be discovered by the human mind. The ancient Chinese, by comparison, believed that the order of nature was inscrutable to the human mind; so they never developed science as a self-correcting, experimental enterprise.
 We need to experiment. The ancient Greeks had organized natural sciences, like Aristotle's biology, as a largely reflective effort. They thought about biology, but they did not investigate biology.
 The order in nature is mathematically precise. Modern science depends on the idea that the order in nature is precise and can be expressed in mathematical formulas; European thought did not see nature as random or haphazard, but rather structured and organized by equations.
These six ideas formed a culture which was the ideal place for a new set of scientific breakthroughs. This is how culture relates to science.