A while back I started writing up an article titled "World's shortest explanation of Gödel's theorem". But I didn't finish it, and later I encountered Raymond Smullyan's version, which is much shorter anyway. So here, shamelessly stolen from Smullyan, is the World's shortest explanation of Gödel's theorem.

@article{WorldsshortestexplanationofGdelstheorem,
key = {WorldsshortestexplanationofGdelstheorem},
type = {article},
title = {World's shortest explanation of G{\"{o}}del's theorem},
author = {Mark Dominus},
abstract = {A while back I started writing up an article titled "World's shortest explanation of G{\"{o}}del's theorem". But I didn't finish it, and later I encountered Raymond Smullyan's version, which is much shorter anyway. So here, shamelessly stolen from Smullyan, is the World's shortest explanation of G{\"{o}}del's theorem.},
comment = {},
date_added = {2020-10-16},
date_published = {2009-01-22},
urls = {https://blog.plover.com/math/Gdl-Smullyan.html},
collections = {about-proof,attention-grabbing-titles,easily-explained,fun-maths-facts},
url = {https://blog.plover.com/math/Gdl-Smullyan.html},
year = 2009,
urldate = {2020-10-16}
}