Department of Mathematics

“Mathematics, in one view, is the science of infinity.” ~P. Davis and R. Hersh. A strong tradition in mathematics is encountering and taming the infinite. We will enter Hilbert’s Hotel to appreciate the intricacies of infinity, and then transition to a formal approach to pinning down what “size” and “infinity” mean. We won’t encounter just one infinity, but a great many of them – so many, in fact, that it defies our notion of size. We’ll also examine some subtleties of our notion of size, discussing the Axiom of Choice and the (Generalized) Continuum Hypothesis.