There are two broad approaches to the world of science; the traditional way, the way of Natural Philosophers is one. Galileo, Newton, Darwin, Adam Smith and many others greats of the past were considered 'Natural Philosophers'. Natural Philosophers observe Nature, and formulate hypotheses and theories based on their observations. They may use mathematics to describe and clarify their observations and hypotheses, but for Natural Philosophers mathematics is simply a tool used to describe Nature.
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