(a) The touchstone of science is experiment. The touchstone of mathematics is proof. Statements in science can never be proved to a certainty, but they assert something factual about the real world. Statements in math can be proved logically, but they only make conditional assertions about the real world, never something directly factual. Thus mathematics is not a science.
A quote from Richard Feynman, Lectures on Physics:
Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.
(b) The root for the word 'science' is the latin 'scientia', which basically means knowledge. Mathematics is certainly a kind of knowledge. Math is so deeply intertwined with physics, and to a lesser but still significant extent with chemistry, biology, and other sciences, that it makes no sense to separate. Thus mathematics is a science.
Supposedly Niels Bohr once said that the opposite of a small truth is a falsehood, but the opposite of a great truth is another truth. Not good for 2-valued logic, but perhaps a good answer to your question.
(Incidentally, Niels Bohr's brother was Harald Bohr, a mathematician of some note.)