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Volume 8, Issue 4

May 14, 2002, saw the publication of Stephen Wolfram's book A New Kind of Science--the culmination of more than twenty years of work by scientist, Mathematica creator, and Wolfram Research CEO Stephen Wolfram. An instant bestseller, the book is being widely read by scientists and non-scientists alike.

Mathematica played several crucial roles in the creation of A New Kind of Science (abbreviated NKS). Most obviously, Mathematica is the notation used in the technical notes in the book--which contain nearly 800 Mathematica programs. Mathematica was also extensively used in the physical production of the book--notably in the creation of the nearly 1000 striking computer graphics that fill the book.

But behind the scenes Mathematica was even more central: it was the main tool that made it possible for the science in NKS to be developed at all.

Stephen Wolfram began the research that eventually led to NKS in the early 1980s. But by the mid-1980s his work was blocked by the lack of adequate computational tools. This was a large part of the reason that he decided to develop Mathematica.

As Wolfram describes it, having Mathematica allowed him to do in only ten years what might otherwise have taken fifty. Wolfram likens one of the roles of Mathematica in NKS to early uses of the telescope. For just as the telescope suddenly opened up a whole host of discoveries in the astronomical world, so Mathematica suddenly opened up a whole host of new discoveries in the computational world of simple programs.

In NKS, Wolfram discusses the connections and implications of his discoveries for a very wide range of issues in mathematics, physics, biology, computer science, and elsewhere. And throughout, he uses Mathematica as a crucial tool to apply both existing and new methods of analysis.

After a break of several years for the development of Versions 1 and 2 of Mathematica, Wolfram began to work in earnest on NKS in 1991. And over the next ten years he used Mathematica intensively every day in his research, altogether running more than a million lines of Mathematica input.

The Programs of NKS

In the main text of NKS Wolfram explains his ideas and discoveries using just ordinary language and pictures. But in the extensive technical notes at the back of the book he uses more technical formalism. And throughout, everything is represented by Mathematica programs.

NKS is in many ways a remarkable showcase of the power of the Mathematica language. The 800 or so programs in NKS cover a huge range of computational functions and concepts--with extremely short and clear programs that make use of the many programming paradigms available in Mathematica.

Mathematica users at all levels will find much to study in the construction and operation of the programs in NKS. Subsequent issues of this journal will contain articles that dissect and discuss some of the programs in NKS. The index to NKS (available online at lists many Mathematica functions, showing where they are used in the programs.

All the programs in the notes to NKS are available online at The programs are presented in notebooks (see example below). In each case, the original form of the program as it appears in the printed version of NKS is given, together with test examples and a version conveniently set up for experimentation.


Coming soon is a new Mathematica-powered product (illustrated below) that allows anyone to reproduce the key graphics from NKS on their own computers, and to do their own experiments on the discoveries in NKS.

NKS Explorer is based on the very same Mathematica programs that Stephen Wolfram used to create the graphics in his book. But using the latest custom Mathematica technology, Wolfram Research will be delivering NKS Explorer as a standalone product.

The form-based interface to NKS Explorer is exclusively built using notebooks and Mathematica's symbolic document capabilities. The simplicity of the interface makes NKS Explorer ideal for a very wide range of users--from experienced scientists to elementary school children.

NKS Explorer--like other Mathematica-powered products such as CalculationCenter--serves as an interesting model for interface development in Mathematica.

NKS Explorer is set up to be able to exchange data with Mathematica. Also coming soon is NKS Explorer Mathematica Kit, which allows functions from NKS Explorer to be run within a Mathematica session.

For more information about NKS, or to order the book, visit

For more information about NKS Explorer, or to purchase the software, visit

Copyright © 2002 Wolfram Media, Inc. All rights reserved.