MathForge links to an article on Hilbert’s “24th” problem. Hilbert, in his famous 1900 speech, proposed twenty-three open problems in mathematics, but apparently there was a twenty-fourth that he dropped from the list, to formalize the notion of simplicity of proofs, and prove that theorems have a unique simplest proof. Like many of Hilbert’s twenty-three, this is less a problem and more an open-ending research program.