The Continuum Hypothesis. An impossible problem. This mind-bending problem literally has no solution - but that doesn't mean we can't resolve it. But doing so will require pushing mathematics beyond anything we now know into new and unexplored territory.
The Continuum Hypothesis was first posed by Georg Cantor, and further developed by David Hilbert. Recently, significant progress has been made and plausible resolutions have been proposed, but the Continuum Hypothesis remains unanswered as one of the most elusive and impossible problems ever in the history of mathematics - one that will require new techniques and new ideas to fully resolve.
Start Here: Sets