and over again I was excited to find that with my new kind of science I could suddenly begin to make great progress—even on problems that in some cases had remained unanswered for centuries.

Given the whole framework I had built, many of the things I discovered seemed in the end disarmingly simple. But to get to them often involved a remarkable amount of scientific work. For it was not enough just to be able to take a few specific technical steps. Rather, in each field, it was necessary to develop a sufficiently broad and deep understanding to be able to identify the truly essential features—that could then be rethought on the basis of my new kind of science.

Doing this certainly required experience in all sorts of different areas of science. But perhaps most crucial for me was that the process was a bit like what I have ended up doing countless times in designing Mathematica: start from elaborate technical ideas, then gradually see how to capture their essential features in something amazingly simple. And the fact that I had managed to make this work so many times in Mathematica was part of what gave me the confidence to try doing something similar in all sorts of areas of science.

Often it seemed in retrospect almost bizarre that the conclusions I ended up reaching had never been reached before. But studying the history of each field I could in many cases see how it had been led astray by the lack of some crucial piece of methodology or intuition that had now emerged in the new kind of science I had developed.

When I made my first discoveries about cellular automata in the early 1980s I suspected that I had seen the beginning of something important. But I had no idea just how important it would all ultimately turn out to be. And indeed over the past twenty years I have made more discoveries than I ever thought possible. And the new kind of science that I have spent so much effort building has seemed an ever more central and critical direction for future intellectual development.