Fourteen Proofs Robin Chapman of the Univesity of Exeter's home page has an interesting paper that gives fourteen proofs that the sum of the reciprocals of the squares of the natural numbers equals pi squared over six (see Evaluating zeta(2) ) Given this result you can tproove another amazing result. If you pick any two positive integers at random, the probability of them having no common divisor is 6 divided by pi squared.