Mathematics is both old and new. Traditionally, research in mathematics is the study of numbers and spaces: numbers such as the natural numbers 1, 2, 3, etc that everyone is familiar with, and spaces such as the 3-dimensional space that we see around us. From a modern viewpoint, one can argue that mathematics is still about numbers and spaces, but then one would have to widen the interpretation of ''numbers'' and ''spaces'' to include the great variety of forms that numbers and spaces have recently evolved into. This is what mathematical research has become.'