Mathematics is the art of highlighting the necessary consequences of a situation. That's all.
The situations that we mathematicians mostly consider are axiomatic constructs, because it's easier to then unambiguously establish necessity.
That this art, its methods, techniques and tools, happens to be so useful to other sciences (and in fact most of human knowledge) is an interesting phenomenon...
> Also, your definition applies to physics as well.
Um.... I think that it looks like that a lot of what maths does is shared with physics, but I think (I could be wrong) that it's mostly because physics has adopted the language of mathematics.
That having been said, there is an aspect where they are definitively different. Physics is motivated by the understanding of the physical world. For instance a physics theory gets dropped when we discover that we mis-observed whatever it was meant to explain. This doesn't happen in maths. The theories in maths (here defined as axiomatic structures) do not need to align with the natural world and get studied for other reasons than because they would increase the understanding of the natural world. Such understanding may eventually happen, but was not the motivation factor.
The situations that we mathematicians mostly consider are axiomatic constructs, because it's easier to then unambiguously establish necessity.
That this art, its methods, techniques and tools, happens to be so useful to other sciences (and in fact most of human knowledge) is an interesting phenomenon...