Mathematica is by any reasonable measure the most advanced computer language currently in widespread use. With its highly general core symbolic architecture, Mathematica incorporates and extends a vast range of advanced language concepts, efficiently implementing them in a full, rich, practical environment with broad systems-level support.
While traditional research languages tend to concentrate on particular language paradigms, Mathematica integrates fully developed symbolic, rule-based, functional, declarative, procedural and other paradigms into an immediately extensible framework. Its clean, unified design leads to unprecedentedly concise and readable code—that is immediately suitable for analysis and exposition.
Crucial to most practical projects is not only Mathematica's built-in access to the world's largest web of mathematical and computational algorithms, but also its full built-in dynamic visualization capabilities, completely customizable user interface—and fully developed interactive notebook documents. Mathematica not only gives a rich and elegant notation for formal descriptions of computational concepts, but also provides a complete practical environment for investigating their consequences.
Increasingly popular in computer science education for its power, immediacy and unique ability to introduce nonexperts to advanced language concepts, Mathematica's symbolic framework allows a new level of experimentation and analysis of algorithms, programming languages, interfaces and other areas of computation.
- Combinators can be implemented in half a line of Mathematica code
- In comparisons, Mathematica is commonly dramatically more concise than almost any other language
- Stephen Wolfram's A New Kind of Science successfully uses Mathematica as its notation throughout