Inspired by the question Does the term “science” encompass humanities and the social sciences?, I would like to ask a question that has been in my mind for decades.
Does "Science" include Mathematics? Or, put in another way, is Mathematics part of Science?
What I understand about Math are: Math is not humanities. Math is not natural science. Math is not social science. If Math is part of science, what kind of science is it?
When people say STEM, do they mean Math is separate from Science? Or they just say it for the sake of convenience?
This is a good question, but there is no consensus as to a good answer. Some people think mathematics is obviously a science, some people think it obviously isn't, and some just aren't sure.
It's common to include mathematics as a special case of science in general discussions. For example, universities usually classify mathematics under the sciences, and "scientific publishing" would generally be understood to include mathematics. However, there are exceptions, and abstract discussions of science often don't apply very well to mathematics.
If this distinction matters in a given case, then you'll have to discuss it explicitly, since you can never assume everyone will agree by default.
If Math is part of science, what kind of science is it?
The most compelling answer I've heard is that it is a formal science. However, this terminology is somewhat obscure, and it is certainly not a consensus answer to your question.
When people say STEM, do they mean Math is separate from Science?
I don't think the intention is to assert that they are definitely separate, but rather just to have an inclusive acronym we can all agree on.