eli5: What is Godel’s Incompleteness Theorem in math and computer science?

Question

What are the problems and theorems that are derived from it?

In: 80

Answer 1

It basically says that any logic system breaks apart when you force it to talk about itself.

For example, “this statement is false”, “what would Pinocchio’s nose do if he says “my nose will now grow”, what to do if you are compelled to accept the mission “mission : reject this mission” and so on.

Of course Godel did it with formal proof for any formal system of logic that can define and perform addition and multiplication of numbers.