I am honored to be giving the 2025 William Reinhardt Memorial Lecture at the University of Colorado Boulder, March 11, 2025.

How we might have taken the Continuum Hypothesis as a fundamental axiom, necessary for mathematics

Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis might easily have been very different than it is. If our mathematical history had been just a little different, I claim, if certain mathematical discoveries had been made in a slightly different order, then we would naturally have come to view the continuum hypothesis as a fundamental axiom of set theory, necessary for mathematics, indispensable even for the core ideas of calculus.