When Is a Mathematical Proof Finished: Construction, checking and the four colour theorem

A mathematical proof can be ready to circulate while further improvements remain possible. Building on Donald MacKenzie’s historical account and its published corrections, this article examines how Appel and Haken connected proof construction with checking, repair and readiness to make their work public. It distinguishes constructing a workable argument, judging it ready to circulate and securing wider mathematical acceptance. An explanatory diagram and vocabulary appendix make these relationships accessible. The article offers neither a universal stopping rule nor a new archival reconstruction.