Full Idea
For intuitionists, truth is not independent of proof, but this independence is precisely what seems to be suggested by Gödel's First Incompleteness Theorem.
Gist of Idea
Gödel's First Theorem suggests there are truths which are independent of proof
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.8)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.168
A Reaction
Thus Gödel was worse news for the Intuitionists than he was for Hilbert's Programme. Gödel himself responded by becoming a platonist about his unprovable truths.