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Arithmetic is strictly dealing with real numbers and operators, (addition, subtraction etc.) Mathermatics covers a much broader description including arithmetic, calculus, algebra, etc... You can say that Arithmetic is a subset of Mathematics.
2 points. Math is the language used to communicate Science. The Science is still there, with or without Math, the question is whether it can be understood or communicated. Math, on the other hand, is a construct used to convey Scientific understanding. Without Science, Math would be useless. That is why the Nobel Prize is not offered for Math, although it is for various Scientific and Economic realms. Moreover, the majority of the most famous Mathematicians were, in fact, Scientists.