Modern electronic computers can provide the numerical solution of systems of one thousand simultaneous nonlinear ordinary differential equations, given a complete set of initial conditions, with accuracy and speed. It follows that as soon as physical, economic, engineering, and biological problems are reduced to the task of solving initial value problems for ordinary differential equations, they are well on their way to complete solution. Hence, the great challenge to the mathematician is to find ways to construct the requisite theories and formulations, approximations and reductions.