Full Idea
At the age of 19 Saul Kripke published a completeness proof of propositional modal logic.
Gist of Idea
Propositional modal logic has been proved to be complete
Source
report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Feferman / Feferman - Alfred Tarski: life and logic Int V
Book Reference
Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.286