From Mathematics to Generic Programming

9. Organizing Mathematical Knowledge

All the truths of mathematics are linked to each other,and all means of discovering them are equally admissible.

Legendre

Now we’re going to look at some of the building blocks for organizing knowledge, particularly mathematical knowledge. We’ll start by exploring the notion of proofs and the introduction of the idea of theorems. Then we’ll examine some important examples of attempts to build up bodies of knowledge from axioms.

Mathematicians have been thinking about how to organize knowledge for thousands of years. As programmers, we will use their organizational principles in our domain of algorithms and data structures.

9.1 Proofs

People had been discovering and using mathematical results long before they ...