Independence of CH: Forcing

In his famous 1900 speech, Hilbert listed the 23 most significant open mathematical problems of his day, and CH held the number one spot. It took two major breakthroughs to find the answer: first, in 1939, Gödel proved that CH is consistent with set theory. Then, in 1963, Cohen proved that “not CH” is also consistent. Cohen developed a powerful new tool, called forcing, to prove this result.