# The Jordan Curve Theorem, Formally and Informally

```@article{Hales2007TheJC,
title={The Jordan Curve Theorem, Formally and Informally},
author={Thomas C. Hales},
journal={The American Mathematical Monthly},
year={2007},
volume={114},
pages={882 - 894}
}```
• T. Hales
• Published 1 December 2007
• Mathematics
• The American Mathematical Monthly
1. INTRODUCTION. The Jordan curve theorem states that every simple closed pla-nar curve separates the plane into a bounded interior region and an unbounded exterior. One hundred years ago, Oswald Veblen declared that this theorem is " justly regarded as a most important step in the direction of a perfectly rigorous mathematics " [13, p. 83]. Its position as a benchmark of mathematical rigor has continued to our day. Many vastly underestimate the logical gulf that separates a typical published…
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