Euclid After Computer Proof-checking

TL;DR

This paper examines Euclid's axiomatic approach in the context of modern computer proof-checking, exploring implications for mathematical rigor, foundations, and the nature of logical truth.

Contribution

It analyzes how Euclid's methods align with contemporary computer-verified proofs, offering insights into the evolution of mathematical rigor and foundations.

Findings

Computer proof-checking enhances rigor in Euclidean geometry

Euclid's axioms are compatible with modern formal verification

The exercise sheds light on the relationship between logic and mathematical truth

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?