In 1963, twenty-five years after Gödel’s proof of the consistency of the CH and the AC, relative to the consistency of ZF, Paul Cohen (1966) proved the consistency of the negation of the CH, and also of the negation of the AC, relative to the consistency of ZF. Thus, if ZF is consistent, then the CH is undecidable in ZFC, and the AC is undecidable in ZF.  To achieve this, Cohen devised a new and extremely powerful technique, called forcing, for expanding countable transitive models of ZF.