Base case for a proof that all natural numbers are interesting: Take zero. Zero is pretty interesting. You can't divide by it, additive identity, if you multiply by it you get zero. All in all, a pretty interesting number. Now consider the set of all totally uninteresting natural numbers. Let n be the smallest element of the set. Now, come on, that's pretty interesting: the smallest totally boring Natural number! So x is actually not uninteresting, and thus there can be no smallest element in the set and the since every nonempty set of natural numbers has a smallest element, the set is empty.
Theorem 2: All numbers are boring.
Proof: Suppose for contradiction that some number is not boring. Who cares?