>> So mathematics is not science?
>
> No, math is not science.

I concur with Darren.

Science is the systematic investigation of the real world. Math is the 
systematic investigation of abstract systems of axioms of an arbitrary 
nature. Some of these systems may or may not be related to something 
that happens in the real world, and as such may be "useful". But there 
is no requirement for that in pure math. (Applied math is another 
matter, of course...)

Some have asserted that "mathematics is the language of science" (which 
is not the same as "mathematics *is* science").

On the other hand, more recently some have suggested mathematics 
becoming an experimental discipline. (After, e.g., the fiasco with the 
4-colour map conjecture and its proof.)

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