No. The scientific method is the foundation of science. Math is a wonderful tool that is used in science and other fields like business, architecture, music, etc.
> Things in science are provable because of the rigorous mathematical proofs applied to data, correlating with reproducible results, is my perception.
Nothing in science is "provable". Science is not math or logic. Go look up what a scientific theory is.
> The point of science is to build a model that can be used to build other models, or ultimately be applied to game the subject.
That is not the point of science. It is a benefit of science but not the point of science.
> Your definition of science seems to only exclude some folks from the term that are doing the exact same work in a different subject.
Not my definition. I didn't make it up. Just because you haven't a clue what science really is doesn't mean it's "my" definition. How about you take a few seconds and relearn what was taught in high school.
You have a bizarre notion that science exists to benefit ourselves. Religion, art, literature, music, business, etc also benefit us. Doesn't make it science.
Society is a human creation with human laws. That is no more "natural law" than the man-made laws governing chess or monopoly are "natural law".
Now that doesn't mean social "science" is worthy of study. Of course, humanities are worthy of study. But it isn't a science. I think politics is just as valid a field of study as physics or art or literature. But it doesn't make political science a science.
But your real worry is that removing science from social science takes away much of the credibility and respect that real scientists in physics, biology, chemistry, etc have earned right? In my experience, it's usually the social "scientists" who are the most vocal about latching onto "science" because they so desperate want cling onto that unearned authority and credibility.
But then again, it's also why creationists ( creation science ) also want to latch on to science. Pretty much frauds who want to manipulate society want something to give them credibility.