Basically, given a proof P of a statement expressed in n bits, you can in polynomial time with respect to n create a new PCP proof Q which spreads out (somehow?) P, including the errors in P. Since the errors are spread out, with high probability, you'll catch an error choosing a very small number of bits of Q.
It's like MAGIC... Especially since they don't explain it at all in the article.
Hmm. According to that, the theorem applies to propositional logic. Propositional logic is a very weak system; I don't think it can state the Riemann hypothesis.
Edit: I take that back: propositional logic definitely can't state the Riemann hypothesis. PropLog is complete, which means that by Goedel's incompleteness theorem it can't even model the natural numbers, much less the complexes.
It's like MAGIC... Especially since they don't explain it at all in the article.
http://en.wikipedia.org/wiki/PCP_theorem