I think it is fair to say that Science is the study of taking observed characteristics of the physical world and putting them into mathematical terms. When thinking of the generic “sciences,” I think of physics, chemistry, and biology, which are all mathematical forms of study devoted to the understanding the world. These, however, are only the natural sciences and limiting the definition of sciences to only natural ones ignores the social sciences. So, what makes science different from the humanities? I think it is appropriate in this case to find what makes the humanities different from social sciences because both the humanities and social sciences attempt to understand humans. I think the difference is how they study humans in that social science attempts to understand why humans act the way that they do, and humanities attempts to understand what is a human. However, I think that the reason mathematics is only really applied to the science because the question of why things happen is rooted in mathematics rather than the question than the what is question that humanities asks.
Important Question: Why is it so difficult to challenge a normative idea in the mathematical, empirically based field of science? Many of these people with contentious, seemingly revolutionary ideas that are properly backed mathematically still received skeptically and punishment.