 The work on the Collatz conjecture shows how far plausibility is from genuine proof.While most mathematicians do not think that probabilistic evidence for the properties of a given object counts as a genuine mathematical proof, a few mathematicians and philosophers have argued that at least some types of probabilistic evidence (such as Rabin's probabilistic algorithm for testing primality) are as good as genuine mathematical proofs.A combinatorial proof establishes the equivalence of different expressions by showing that they count the same object in different ways.