Editing Mathematical proof (section)

==Undecidable statements==
A statement that is neither provable nor disprovable from a set of [[axiom]]s is called undecidable (from those axioms). One example is the [[parallel postulate]], which is neither provable nor refutable from the remaining axioms of [[Euclidean geometry]].

Mathematicians have shown there are many statements that are neither provable nor disprovable in [[Zermelo–Fraenkel set theory with the axiom of choice]] (ZFC), the standard system of set theory in mathematics (assuming that ZFC is consistent); see [[List of statements undecidable in ZFC]].

[[Gödel's incompleteness theorem|Gödel's (first) incompleteness theorem]] shows that many axiom systems of mathematical interest will have undecidable statements.