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The article discusses the role of computers in nonlinear science. The term experimental mathematics has been coined to describe computer-based investigations into nonlinear problems that are inaccessible to analytic methods. The experimental mathematician uses the computer to simulate the solutions of nonlinear equations and thereby to gain insights into their behavior and to suggest directions for future analytic research. Nonlinear science has become a discipline in itself, simply because nature is intrinsically nonlinear. The term nonlinear science, meaning the science of problems that are not linear, may seem odd at first. It seems to suggest that linear problems are the central issue, while in fact precisely the opposite is true. Although simple dynamical systems with low dimensional phase spaces can model much of the real world, the analysis of many physical phenomena requires a somewhat different approach. Digital computers, at both mainframe and minicomputer levels and in the conventional sequential or partially pipelined architecture, remain the general purpose tool of experimental mathematicians.