Euclid After Computer Proof-checking

Abstract

Euclid pioneered the concept of a mathematical theory developed from axioms by a series of justified proof steps. From the outset there were critics and improvers. In this century the use of computers to check proofs for correctness sets a new standard of rigor. How does Euclid stand up under such an examination? And what does the exercise have to teach us about geometry, mathematical foundations, and the relation of logic to truth? 4 See [32] (Prologue). But by 1902, when Russell was thirty, he had changed his mind, and published an article pointing out errors in Euclid I. 1, I.4, I.7, and I.16 [31].