Abstract. Gödel's Incompleteness Theorem states that any axiomatization of number theory will miss something; that there will always be a number-theoretic statement that is true and yet unprovable. Along with several other celebrated theorems of logic it sets mathematics apart from all other human endeavors - unlike in physics, economy or history, we mathematicians know our foundations. We have an extremely good collection of axioms so we know what we can do. And we even know, quite for sure, what we will never be able to do - prove all that is right, for one.
Gödel's theorem is famed even outside of math, yet not enough of us know how easy it is. Indeed, here's that statement that is true and yet unprovable:
Self reference? Maybe. But remember,
Come to my talk and see how all these facts fit together!