This project is the 1988 Centennial Symposium which is to focus on the topic "Mathematics into the Twenty- first Century" and to be held during the Centennial Meeting of the American Mathematical Society in Providence, Rhode Island in August of 1988. The purpose of the meeting will be to provide a comprehensive survey of the significant fields of mathematics. The talks will be of a nature understood by a general mathematical audience and will examine the motives, paradigms, and prospects of major areas of contemporary mathematical research. The research topics to be presented include: Finite simple groups, nonlinear elliptic partial differential equations, probability and statistics, mathematical physics, low dimensional topology, mathematical logic, algebraic number theory, algebraic geometry, representation theory of p-adic groups, von Neumann algebras and knot theory, nonlinear hyperbolic equations, mathematical biology, algebraic K- theory, dynamical systems and Kleinian groups, theoretical computer science and combinatorics, and calculus of variations.