Euclid After Computer Proof-checking
arXiv:2103.09623 · doi:10.1080/00029890.2022.2069985
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?
25 pages, 16 figures. To appear in American Mathematical Monthly in 2022