Building a Library of Mechanized Mathematical Proofs: Why Do It? and What Is It Like to Do?

Abstract

A few years ago I used the ProofPower mechanized proof tool to develop the calculus from the ε − δ definitions of limits through to the derivation of the properties of the trigonometric functions from their differential equations. At the time, I wrote:

“Undertaking this kind of work is a mathematical activity of an unusual, often entertaining, albeit sometimes frustrating nature. It is rather like preparing the material for a course or a textbook with the assistance of an amanuensis who is an idiot savant of an unusual kind. Firstly, he insists on and gets absolute editorial control over what purports to be a proof: every proof step is checked with complete accuracy and no lacunae slip his attention. On the more constructive side, he [can be] capable of amazing feats of calculation.”

In this talk, I will discuss what it is like to develop mathematical theories with such an unusual assistant and on why the results will eventually be seen as highly worthwhile for mathematicians, computer scientists and engineers.