Mathematica is a computer program for doing mathematics. It is often used for instruction, homework, research, and writing. Mathematica is extraordinary well-rounded. It is suitable for both numeric and symbolic work, and it has remarkable word-processing capabilities as well. Mathematicians can (and often do) search for a working model, do intensive calculation, and write a dissertation on the project (including complex graphics) — all from within Mathematica.
Its weaknesses include a somewhat steep learning curve, an interface that is difficult to use from the command line, and rather complex installation procedures.