Mathematics and Nature

Is any area of mathematics sacred?
That is to say are there any areas of mathematics which are pure abstractions.
(Or to put it more bluntly are the Pure Mathematicians really doing applied mathematics and they just don't know it yet?)As a possible avenue of this discussion, what are we doing when we say we are doing mathematics.(I'm not sure where to put this, maybe "Is it Science?", or perhaps Coffee House would be better.")

I am asking is there any area of current pure mathematical research which will escape being subsumed into physical theory.
Rather than asking is Maths a Science, I am asking is there any area of Pure Mathematics which is of no used to Science, especially physics.Over the last century we have seen areas we thought useless to physics, such a noncommutative geometry actually come into play in the physical sciences.Does Pure Mathematics mean no more than Mathematics with no current use.