**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,

- Number theory contains computer science; indeed, all that computers can do is to crunch numbers!
- A proof given in full detail can be verified by a computer.
- One can write a computer program that prints itself. Even, itself followed by the entire Unabomber Manifesto.

Come to my talk and see how all these facts fit together!

**References.**

- According to this Time Magazine article, Gödel is one of the 100 Most Important People of the Century (the previous century, I presume).
- Gödel's biography at The MacTutor History of Mathematics archive. (Gödel died on January 14th, 1978, 27 years ago tomorrow).
- Gödel's original 26 page article in HTML, in PDF and as an 80 page booklet on Amazon.
- An excerpt from Rudy Rucker's Infinity and the Mind.
- westley.c: an obfuscated (see also) C program by Brian Westley, that plays Tic Tac Toe on its own code.
- An article by David Boozer on Programs That Print Themselves Out. (Some shorter, longer and funnier examples are here).
- A little on Gödel's second incompleteness theorem.