Mathematics is an exact language for description, calculation, deduction, modelling, and prediction — more a systematic way of thinking than a set of rules.
Mathematically educated people are stem cells of the technologically advanced society. Because of universality of mathematics, mathematicians are flexible and armed with tools for work in technological environments which never existed before.
At a personal level, mathematics is the music of reason. Learning mathematics involves deep assimilation of aesthetic criteria and efficient patterns of thinking.
This should be perhaps be read in conjunction with Definition of Mathematics, according to Confederation of British Industry.
Your opinion? Please give your definition /description of mathematics.