Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations

Theorem distributions [in standard mathematics]

The picture below shows which of the possible theorems from page 812 hold for each of the numbered standard mathematical theories from page 805. The theorem close to the right-hand end valid in many cases is (p p) p p (p p). The lack of regularity in this picture can be viewed as a sign that it is difficult to tell which theorems hold, and thus in effect to do mathematics.

Image Source Notebooks:

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