Editing Mathematical proof (section)

===Probabilistic proof===
{{Main|Probabilistic method}}
A probabilistic proof is one in which an example is shown to exist, with certainty, by using methods of [[probability theory]]. Probabilistic proof, like proof by construction, is one of many ways to prove [[existence theorem]]s.

In the probabilistic method, one seeks an object having a given property, starting with a large set of candidates. One assigns a certain probability for each candidate to be chosen, and then proves that there is a non-zero probability that a chosen candidate will have the desired property. This does not specify which candidates have the property, but the probability could not be positive without at least one.

A probabilistic proof is not to be confused with an argument that a theorem is 'probably' true, a 'plausibility argument'. The work toward the [[Collatz conjecture]] shows how far plausibility is from genuine proof, as does the disproof of the [[Mertens conjecture]]. 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 [[primality test|testing primality]]) are as good as genuine mathematical proofs.<ref>Davis, Philip J. (1972), "Fidelity in Mathematical Discourse: Is One and One Really Two?" ''American Mathematical Monthly'' 79:252–63.</ref><ref>Fallis, Don (1997), "The Epistemic Status of Probabilistic Proof." ''Journal of Philosophy'' 94:165–86.</ref>