Full Idea
Tarski's Theorem states that under fairly generally applicable conditions, the assumption that there is a definition of truth within a given theory for the language of that same theory leads to a contradiction.
Gist of Idea
Tarski proved that truth cannot be defined from within a given theory
Source
report of Alfred Tarski (The Concept of Truth for Formalized Languages [1933]) by Volker Halbach - Axiomatic Theories of Truth 1
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.4
A Reaction
That might leave room for a definition outside the given theory. I take the main motivation for the axiomatic approach to be a desire to get a theory of truth within the given theory, where Tarski's Theorem says traditional approaches are just wrong.
Related Ideas
Idea 16303 Tarski made truth respectable, by proving that it could be defined [Tarski, by Halbach]
Idea 14968 A weakened classical language can contain its own truth predicate [Gupta]
Idea 14796 Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce]