MADNESS provides a high-level environment for the solution of integral and differential equations in many dimensions using adaptive, fast methods with guaranteed precision based on multi-resolution analysis and novel separated representations. There are three main components to MADNESS. At the lowest level is a new petascale parallel programming environment that increases programmer productivity and code performance/scalability while maintaining backward compatibility with current programming tools such as MPI and Global Arrays. The numerical capabilities built upon the parallel tools provide a high-level environment for composing and solving numerical problems in many (1-6+) dimensions. Finally, built upon the numerical tools are new applications with initial focus upon chemistry, atomic and molecular physics, material science, and nuclear structure. WWW: https://github.com/m-a-d-n-e-s-s/madness