Science has two important characteristics.
1) The use of the scientific method of theorising based on empirical data gained from rigorous and repeatable experimentation. 2) Using this method to create theories to explain natural phenomena.
Mathematics doesn’t do either of those things. Theorems are proved logically not empirically, and maths is not concerned with the natural world.
Science uses maths as a tool but that does not make maths a science, anymore than drawing is a science because a physics paper includes a diagram.
Mathematics is the creation and study of beautiful things, i.e. theorems and proofs. It’s an art, not a science.