Mathematica is a general computing environment, organizing many algorithmic, visualization, and user interface capabilities within a document-like user interface paradigm. It was originally conceived by Stephen Wolfram, developed by a team of mathematicians and programmers that he assembled and led, and it is sold by his company Wolfram Research.

Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. It is this range of capabilities – many world-leading in their own right – that makes Mathematica uniquely capable as a "one-stop shop" for you or your organization's technical work.
Mathematica combines powerful computing software with a convenient user interface. Mathematica's features include symbolic and high-performance numeric computation, 2D and 3D data visualisation, broad programming capabilities, and one-step creation of web documents. Mathematica's notebook format allows for the generation of cross-platform, fully customisable files that provide professional mathematical typesetting and publication-quality layout of electronic and printed media.

Features of Mathematica:
• Vast web of mathematical, visualization, graphics, and general programming functions, typically with state of the art implementations
• Ability to instantly create user interfaces to arbitrary computations by just specifying parameters
• Integrated computable data sources, from chemistry and pure mathematics to city locations and country statistics
• Highly general interface that allows the uniform manipulation and intermingling of graphics, programs, user interfaces etc
• Support for efficient datastructures such as sparse arrays, piecewise functions, etc
• Support for emerging fields such as graph plotting and analysis, alternate input devices, new data formats
• Ability to create and publish programs that run on the free Mathematica Player

Mathematica is split into two parts, the "kernel" and the "front end" . The kernel is the algorithmic engine for performing computations. The front end provides a convenient human interface for creating and manipulating programmatic structures, allowing graphics, mathematics, programs, text, and user interfaces can be freely edited and intermingled. It also provides debugging capabilities, a presentation environment, and interfaces to usb controllers like gamepads. The two communicate via the MathLink protocol. It is possible to use the kernel on one computer and the front end on another, although this is not how most people use Mathematica.

Key Elements of Mathematica:
• Notebook Document System
• Complex Analysis
• Volumes of Knowledge
• Typesetting
• Symbolic and Numeric Computations
• Graphics
• Application Development
• Programmable Palettes
• Special-Purpose Interfaces
• Programming Language
• Interactive Help Browser

A distinguishing characteristic of Mathematica, compared to similar systems, is its attempt to uniformly capture all aspects of mathematics and computation, rather than just specialized areas. The main innovation that makes this possible is the idea of symbolic programming captured in the Mathematica programming language, emphasing the use of simple tree-like expressions to represent knowledge from a large number of domains. With Mathematica 6, the generality of this approach extends far beyond mathematics, allowing one for example to use graphics and even running programs and paste them in as arguments to functions in a piece of code.

Building on two decades of world-class algorithm and software development, Mathematica 6 represents a dramatic breakthrough that immensely broadens Mathematica's scope and applicability - and redefines the very way we think about computation. Made possible by Mathematica's unique symbolic architecture, Mathematica 6 introduces a sweeping unification of language and interface concepts that makes possible a new level of automation in algorithmic computation, interactive manipulation and dynamic presentation - as well as a whole new way of interacting with the world of data.

Mathematica 6.0 fundamentally redefines Mathematica and introduces a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, Version 6.0 adds nearly a thousand new functions—almost doubling the total number of functions in the system—dramatically increasing both the breadth and depth of Mathematica's capabilities, as well as introducing hundreds of major original algorithms, and perhaps a thousand new ideas, large and small.

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