The Supercomputing Engine for Mathematica enables Wolfram Research's Mathematica to be combined with the programming paradigm of today's supercomputers. Closely following the industry-standard Message-Passing Interface (MPI), this new toolkit creates a standard way for every Mathematica kernel in the cluster to communicate with each other directly while performing computations. In contrast to typical grid implementations of Mathematica that are solely master-slave, this solution instead has all kernels communicate with each other directly and collectively the way modern supercomputers do. After creating an "all-to-all" communication topology using Mathematica kernels on a cluster, the new technology supports low-level and collective MPI calls and a suite of high-level calls, all within the Mathematica computing environment. We present the technology's API, structure, and supporting technologies with examples of its potential application. http://daugerresearch.com/pooch/mathematica/