Abstract:Scientific Computing understands and solves complex scientific and engineering problems using advanced computational capabilities.It integrates the studies of modeling,algorithm,software,and simulation and becomes the indispensable link and tool of the application of modern high performance computer in science and technology.Computation,together with the theory and experiment,has become the main method in current worldwide science and technology innovations.In this paper,we first briefly review the history and development of computational mathematics and scientific computing.Then we introduce the main research directions and recent development of computational mathematics in four fields: numerical algebra,numerical approximation,optimization method,and numerical methods for differential equations.Finally we propose several suggestions on further developing scientific computing in China.