Gödel's incomplete theorems are famously profound, strange, and interesting pieces of math. But it's hard to understand them, and especially hard to understand why they are true. I've never been quite satisfied with the explanations I've seen for the general public, so I wanted to take a crack at explaining what these theorems say and give a flavor of why they hold. See what you think: Incompleteness Theorem 1 is about whether all mathematical truths can be proven. The first inco...