PROMYS provides a lively mathematical environment in which ambitious high school students explore the creative world of mathematics. Through their intensive efforts to solve a large assortment of unusually challenging problems in Number Theory, the participants practice the art of mathematical discovery – numerical exploration, formulation and critique of conjectures, and techniques of proof and generalization. More experienced participants may also study The Mathematics of Computer Graphics, Complex Analysis in Number Theory (Dirichlet’s theorem on arithmetic progressions), and Geometry and Symmetry. Problem sets are accompanied by daily lectures given by research mathematicians. In addition, a highly competent staff of 20 undergraduate counselors live in the residence halls and are always available to discuss mathematics with students. Advanced participants also develop independent research projects advised by research mathematicians. Special lectures by outside speakers offer a broad view of mathematics and its role in the sciences and in future career options.