Stephen Wolfram
Mathematica was developed by Stephen Wolfram, a distinguished polymath educated at Eton, Oxford and Caltech who received his PhD in theoretical physics at the age of 20, and whose work is now cited in over 10,000 technical papers.

Aim
Mathematica aims to provide users with a fully comprehensive integrated environment for all kinds of mathematical application, ranging from elementary computations and transformations to large development projects building mathematical models for use in complex engineering projects.

Approach
Through an interactive programming language optimised for this kind of work, users have access to a comprehensive range of mathematical functions including both the well known standard functions such as sin and cos and Mathematica superfunctions such as Solve, Integrate, and Simplify.

Superfunctions
These superfunctions use the full range of lower level capabilities for certain kinds of problem solving, selecting and applying them as required by the problem in hand.
These superfunctions include "Solve" for exact symbolic and "NSolve" for numeric solution of polynomial equations, "Integrate" for symbolic and "Nintegrate" for numerical integration, "DSolve" and "NDSolve" for simultaneous differential equations, and "Simplify" for simplifying mathematical expressions.

Application Libraries
The power of Mathematica and other computer algebra tools is to a large extent due to the extensive libraries which provide their comprehensive knowledge of mathematics and its applications.
The libraries provided by the supplier are supplemented by compendious online libraries of applications made available by the community of users.


History
Wolfram's interest in computer algebra started with the development of SMP a computer algebra system which he began to develop in 1979 and released commercially in 1981.
After a digression to found the field of complex systems Wolfram returned to computer algebra in 1986 and began the development of Mathematica.
He founded Wolfram Research in 1987 to continue the commercial development of Mathematica.
When first released in 1988, Mathematica seized the lead in this field which it has retained to this day, reaching 100,000 users in 1990 and one million in 1995.

Numerical Computation
Numerical computation in Mathematica is conducted to arbitrary precision controlled by the user.
The user selects the precision he requires in the result and Mathematically automatically selects the precision needed in intermediate results to give that precision in the end result.

Mathematical Libraries
The combination in Mathematica's programming language of those features found in other good high level programming languages together with an exhaustive knowledge of mathematics makes for outstanding ease in implementing mathematical applications.
Alongside these comprehensive mathematical capabilities mathematica provides powerful graphical and multimedia capabilities.
All of this is supported in a document oriented paradigm in which work is prepared and presented in Mathematica "notebooks", suitable either for electronic (fully animated viewing) or hard copy presentation.

