Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations

Invention versus discovery in mathematics

One generally considers things invented if they are created in a somewhat arbitrary way, and discovered if they are identified by what seems like a more inexorable process. The results of this section thus strongly suggest that the basic directions taken by mathematics as currently practiced should mostly be considered invented, not discovered. The new kind of science that I describe in this book, however, tends to suggest forms of mathematics that involve discovery rather than invention.

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