From same youtube

Impossible Programs (The Halting Problem) https://www.youtube.com/watch?v=wGLQiHXHWNk

Math's Existential Crisis (Gödel's Incompleteness Theorems) https://www.youtube.com/watch?v=YrKLy4VN-7k

Gödel's First Incompleteness Theorem, Proof Sketch https://www.youtube.com/watch?v=svOTZEbj3ys

Gödel's Second Incompleteness Theorem, Proof Sketch https://www.youtube.com/watch?v=7fvkbvWaRPk