For a math program, Mathematica shows up in some unlikely enterprises. Japanese fashion designer Eri Matsui used Mathematica to create clothing designs. Science columnist John Cramer used Mathematica to produce a 100-second simulation of the sound of the Big Bang during the first 760,000 years of the universe, rendering mathematical functions as sound that could be captured on .wav files. And a gaming company has used the program to separate people from their money by designing betting games tailored to specific regions.

Mathematica was created by Stephen Wolfram, one of those for whom the label 'boy genius' was invented: publishing his first paper on particle physics at 15, graduating from Caltech with a Ph.D. in theoretical physics at 20, and becoming the youngest person to receive a 'genius' grant from the Macarthur Foundation a year later.

Wolfram developed Mathematica to aid in his own researches, expanding it as a programming language and releasing it as an 'all-in-one' technical computing package in 1988. The software had no parallel, and Wolfram made millions, which in turn enabled him devote his energies to his own scientific work, self-published with a great deal of fanfare in 2002 under the title "A New Kind of Science." Starting by analyzing cellular automata, Wolfram went on to describe, basically, a new kind of science, with computation taking over the role played by calculation in the last couple hundred years. The book, as would be expected of a work laying claim to a significant shift in science, has been the subject of a fair amount of debate.

The software, on the other hand, has generated relatively little debate, except for variations on the theme of how useful it is. Nearly 15 years after Mathematica's introduction, Wolfram Research released Mathematica 5 last year, with much improved and faster numerics capabilities.

Mathematica has been known as much for the breadth of what it can do as the power of the program. From its inception, it was designed to be a complete system for doing mathematics, incorporating symbolics, numerics, graphics, and word processing. The range of uses for Mathematica is extensive. It can handle complex symbolic calculations involving hundreds of thousands or millions of terms; analyze and visualize data; solve equations, including differential equations, and minimization problems numerically or symbolically; and do numerical modeling and simulations, such as those involving financial derivatives, complex biological systems, chemical reactions, or environmental impact studies.

Roger Germundsson, director of R&D at Wolfram, says of the first version of Mathematica, "When it first came out in 1988, it was a bit of a breakthrough. It integrated several different areas into one program - symbolic, numeric, programming, and document. All the areas of technical computing in one program."