I'll endeavor to clarify some basic tenets:

Natural Science refers to acquired knowledge on what exist in Nature. When such knowledge is applied , i.e., is utilized to obtain a benefit, we talk about Applied Science. Mathematics does not exist in Nature, therefore, it is not a Science, yet it should be realized that the more mathematics is applied to a Science, the more exact it becomes. Medicine, as an example, is called an art, yet it is day by day approaching more the status of Science, as more digital technology is invented, including the automated designing of therapeutic agents.

There can be no life without order. The second Law of Thermodynamics --Entropy, the natural tendency to disorder-- is called The Supreme Law of the Universe. Energy is applied by living organisms to oppose entropy. The myths of creation, like that of Genesis, deal with the imposition of order to end chaos. At the time of Aristotle, a vast body of knowledge had accumulated; however, it was he who classified that knowledge. In this way he introduced order in knowledge, gaining justly the honor of being the first scientist.

Philosophy claimed as its domain the areas virgin of Science, having therefore shrunk at the onslaught of the latter. Yet, without the creation of Philosophy there would have not existed Science. It was Thales of Miletus who declared that one matter is Mount Olympus with its gods, and another is what happens down here, meaning, man should think not in terms of godly acts, but in terms of natural acts obeying non-godly --natural-- causes.