Mathematics isn't a humanity but it isn't a science either. It's purer than a science, demanding logical proof, not just evidence.
reminds me of a quote from Sipser's Theory of Computation textbook, towards the beginning. He says something like "in mathematics, not even evidence is enough."
Fair, I'd say it is better to be idosyncratic and consistent than conforming and incongruent. "Formal science" does not make any sense as a subcategory of science if the definition of science basically omits anything that makes mathematics and philosophy what it is. The "formal sciences" do not use the scientific method, and are basically completely distinct from the natural and social sciences in the ways they generate knowledge. In my language, it is generally linked to the humanities, but I'm not hard set on that.
Most mathematics is built on pure reasoning, not experiments. Calling it a science is a bit of a downgrade.