Science of arbitrary structures.
This is a somewhat tendentious definition, in
that there are quite a few other definitions of what mathematics is or is about
that also seem somewhat adequate, and perhaps also somewhat inadequate. One
merit of the given definition is that it makes clear that everything - that
has or is some structure, but what hasn't? - is somehow also studied by
mathematics, that may contain a lot of provable statements about those kinds
of structures, or aspects of them.
Something to the effect of the above definition was proposed by a number of
French mathematicians, who cooperated under the
alias of "Nicholas Bourbaki". A readable and interesting book that
expounds these ideas is Frederik Muller's "Structures for everyone".