Lesson 2

Gödel's First Incompleteness Theorem can be stated informally as follows: There exist true statements that are impossible to prove. (In any consistent formal system strong enough to axiomatize arithmetic.) In other words, we will never know everything with certainty; there will always be true statements that cannot be proven. For example, it is not excluded that the Twin primes conjecture is true, but we will never be able to prove this.