by the mid-1980s, many applications had been found in physics, biology, computer science, mathematics and elsewhere. And indeed some of the phenomena I had discovered were starting to be used as the basis for a new area of research that I called complex systems theory.

Throughout all this, however, I had continued to investigate more basic questions, and by around 1985 I was beginning to realize that what I had seen before was just a hint of something still much more dramatic and fundamental. But to understand what I was discovering was difficult, and required a major shift in intuition.

Yet I could see that there were some remarkable intellectual opportunities ahead. And my first idea was to try to organize the academic community to take advantage of them. So I started a research center and a journal, published a list of problems to attack, and worked hard to communicate the importance of the direction I was defining.

But despite growing excitement—particularly about some of the potential applications—there seemed to be very little success in breaking away from traditional methods and intuition. And after a while I realized that if there was going to be any dramatic progress made, I was the one who was going to have to make it. So I resolved to set up the best tools and infrastructure I could, and then just myself pursue as efficiently as possible the research that I thought should be done.

In the early 1980s my single greatest impediment had been the practical difficulty of doing computer experiments using the various rather low-level tools that were available. But by 1986 I had realized that with a number of new ideas I had it would be possible to build a single coherent system for doing all kinds of technical computing. And since nothing like this seemed likely to exist otherwise, I decided to build it.

The result was Mathematica.

For five years the process of building Mathematica and the company around it absorbed me. But in 1991—now no longer an academic, but instead the CEO of a successful company—I was able to return to studying the kinds of questions addressed in this book.

And equipped with Mathematica I began to try all sorts of new experiments. The results were spectacular—and within the space of a few months I had already made more new discoveries about what