The True (?) Story of Hilbert's Infinite Hotel

Abstract

What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre consequences of assuming an actual infinity of objects or events. Since the 1970s it has been used in a variety of arguments, some of them relating to cosmology and others to philosophy and theology. For a long time it has remained unknown whether David Hilbert actually proposed the thought experiment named after him, or whether it was merely a piece of mathematical folklore. It turns out that Hilbert introduced his hotel in a lecture of January 1924, but without publishing it. The counter-intuitive hotel only became better known in 1947, when George Gamow described it in a book, and it took nearly three more decades until it attracted wide interest in scientific, philosophical, and theological contexts. The paper outlines the origin and early history of Hilbert's hotel paradox. At the same time it retracts the author's earlier conclusion that the paradox was originally due to Gamow.