Full Idea
Gödel's proof wrought an abrupt turn in the philosophy of mathematics. We had supposed that truth, in mathematics, consisted in provability.
Gist of Idea
Prior to Gödel we thought truth in mathematics consisted in provability
Source
report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Willard Quine - Forward to Gödel's Unpublished
Book Reference
Quine,Willard: 'W.V. Quine: Quine in Dialogue' [Harvard 2008], p.157
A Reaction
This explains the crisis in the early 1930s, which Tarski's theory appeared to solve.