Did Paul Cohen "settle" the Continuum Hypothesis? Paul Cohen proved the Continuum Hypothesis is independent of ZFC and concluded that it's truth or falseness is undecidable (1963). Is this still the case today? These links suggest there is still interest in proving or disproving it. http://www.gauge-institute.org/cantor/HilbertFirstProblem.pdf http://www.ams.org/notices/200106/fea-woodin.pdf EDIT: I'm suspicious of the the first link. I can't find out much about the Gauge Institute except that it's located in St Paul,MN and I don't think this paper proves anything, but I'm not a mathematician.