Mathematics is the academic discipline and it's supporting body of knowledge, that involves the study of such concepts as quantity, structure, space and change. "A mathematician, like a painter or a poet, is a maker of patterns." G.H. Hardy
Pure mathematicians work on abstract problems independent of any practical applications - they create new mathematics, build new mathematical structures, and unravel new mathematical patterns. Because it grows out of internal motivations to create, this aspect of mathematics is often likened to art. However, mathematical research developed without reference to real-world problems often ends up being extremely useful in practical situations. Pure mathematicians find employment at universities, government agencies such as the National Security Agency, or companies such as Bell Labs. Resource: American Mathematical Society.