I first came to know about Gödel's incompleteness theorem while watching a video by Veritasium (https://www.youtube.com/watch?v=HeQX2HjkcNo), it's around 30 minutes but a really good video. It's from the time before Veritasium became slop. The video talks about many things that are interconnected, like the halting problem, undecidable systems like the game of life, Hilbert's dream of a finite set of axioms to prove all mathematics, and, of course, a perfect explanation of Gödel's incompleteness theorems