• Mathematics is the study of shape and form, of numbers and patterns, of concrete examples and abstract generalizations. As a discipline mathematics is not easy to categorize. It is an art: there is great beauty in its execution and exposition. It is a science: it is extremely rigorous and it has an experimental aspect. It is pure: within mathematics, one can create a whole universe and explore its properties.
  • It is applied: many of the best ideas of mathematics arise from attempts at solving everyday problems, and some of its most pure concepts have surprisingly practical applications. It is a philosophy: mathematics is grounded in ideas. Most of all, mathematics is alive.