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Mathematica is a computational engine. It is probably the closest tool we have to an effective universal computer in its broadest sense.
Mathematica is the pinacle of Wolfram research, the company built by Stephen Wolfram, initially to develop Mathematica, now with extended ambitions in various areas of computational interest (see a new kind of science and Wolfram|Alpha as other major examples).
The main one is that it is proprietary code.
The most annoying practical feature of Mathematica is that it does not have a good text editor, although this is fundamental for anything related to code editing ("writing code"). Particularly crippling is the inability to split windows, to work on remote aspects of the computation in parallel. Someone reports that:
The following trick—using a palette that makes a duplicate, read-only copy—is useful:I asked this split screen question to Wolfram in 1994! He tried and convince me I didn't need it.
CreatePalette[Button["Duplicate Active Notebook",
NotebookPut[NotebookGet[InputNotebook[]] /.
{Rule[DockedCells, _] :> Sequence[],
Rule[WindowMargins, _] :> Rule[WindowMargins, {{0, Automatic}, {0, Automatic}}],
Cell[x___] :> Cell[x, Evaluatable -> False]},
Background -> GrayLevel[0.95], Editable -> False, "ClosingSaveDialog" -> False,
DockedCells -> With[{sourcenb = InputNotebook[]},
Cell[BoxData[ToBoxes[Button["Update",
SelectionMove[InputNotebook[], All, Notebook];
NotebookWrite[InputNotebook[],
NotebookGet[sourcenb] /. Cell[x___] :> Cell[x, Evaluatable -> False]]]]],
"DockedCell", CellContext -> Cell]],
WindowTitle -> "Duplicate of " <> AbsoluteOptions[InputNotebook[], WindowTitle][[1, 2]]];
SetSelectedNotebook[InputNotebook[]]], WindowTitle -> "Duplicate"];