There was this thread a while back: https://news.ycombinator.com/item?id=25115746 (direct link: https://stopa.io/post/269)

As someone with limited math knowledge, I found it quite readable and understandable though I can't vouch for its accuracy.

I would say, though, when talking about Godel, there is significant disagreement over what his work implies about the world or about the status of truth statements (if anything). You can see people arguing over that in the comments.

edit - this one looks good too, maybe better as it avoids the controversial philosophical discussion: https://dvt.name/2018/03/12/godels-first-incompleteness-theo...

In traditional HN style, I will now thumb my nose at Vertasium's excellent video due to him skipping over how godel came up with the proof.

He built up the whole damn video for that one moment, when he says "And godel went through all this trouble to come up with this card..." and flips over the card. But how godel did it is at least as cool as the proof itself.

I'm mostly being tongue in cheek with the Veritasium nose-thumbing. But if you saw it and want to understand it more deeply (and in my opinion more satisfyingly), I recommend "What Godel Discovered": https://news.ycombinator.com/item?id=25115746

It explains Godel's proof using Clojure. Quite accurately, too.

The thread is also hilarious. Shoutout to the MIT professor who took offense at someone linking to his wikipedia page: "Wikipedia is contentious and often potentially libelous." ... and then you check his wikipedia page, and it's a super positive article about all of his discoveries and life's work.