Sinapse, a knowledge-based, domain-specific system for synthesizing mathematical-modeling software, is discussed. Sinapse generates Fortran-77, Connection Machine Fortran, or C programs from specifications of mathematical equations and numerical methods. The synthesis process is divided into phases of refinement that attempt to duplicate the users' problem-solving processes in the design, implementation, and evolution states of mathematical modeling. These phases, with automated implementation, help modelers increase their productivity because they can write concise specifications and quickly experiment with variations on their models and algorithms by modifying specifications rather than implementations.