What does Godël’s Incompleteness Theorem actually mean and imply? I just saw Ted-Ed’s video on this topic and didn’t fully understand what it means or what the implications of this are.

Question

What does Godël’s Incompleteness Theorem actually mean and imply? I just saw Ted-Ed’s video on this topic and didn’t fully understand what it means or what the implications of this are.

In: 742

Answer 1

For a long time in mathematics the words *true* and *provable* meant the same thing.

Godel showed that they are not. There can be true statements that are unprovable.