Chapter 4: Systems Based on Numbers

Section 10: Continuous Versus Discrete Systems

History [of continuous versus discrete mathematics]

From the late 1600s when calculus was invented it took about two centuries before mathematicians came to terms with the concepts of continuity that it required. And to do so it was necessary to abandon concrete intuition, and instead to rely on abstract mathematical theorems. (See page 1149.) The kind of discrete systems that I consider in this book allow a return to a more concrete form of mathematics, without the necessity for such abstraction.

From Stephen Wolfram: A New Kind of Science [citation]