Mathematica is a tool for technical computing that is used by mathematicians, engineers, analysts, and many others around the world.Mathematica is renowned as the world’s ultimate application for computations. But it’s much more, It contains an extensive knowledge base for working with a very broad range of tasks, including solving equations, programming, importing and exporting data, visualizing functions and data, and much more.
Grasshopper is providing a graphical algorithmic process for generating computational models through a mapping process of design objectives onto step-by-step descriptions. In addition, GH enables extracting any parametric data of the process to recognize patterns of geometric behavior, and can makeup multiple relations between the parameters in the algorithm.
A tool for Grasshopper named Mantis which allows to interact with Mathematica directly.. If you are interested to know more about the integration between GH & Mathematica via Mantis, follow http://www.grasshopper3d.com/group/mantis
Here is a couple of examples: