Mathematics is both an art and a science: There is great beauty in its execution and exposition, and it is rigorous and 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 also a philosophy, as mathematics is grounded in ideas. Most of all, mathematics is alive. It has engaged human thought for millennia and remains a vibrant and growing area of human endeavor with new and important discoveries. Faculty in the department examine the art, science, application and philosophy of mathematics. Here, you can see a sampling of their research.