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

TL;DR

This paper explores the origin and historical development of Hilbert's hotel paradox, clarifying its true origins and its role in illustrating the counterintuitive properties of infinite sets in mathematics and philosophy.

Contribution

It uncovers the true origin of Hilbert's hotel, showing it was first introduced by Hilbert in 1924 and clarifies misconceptions about its authorship.

Findings

Hilbert introduced the hotel in a 1924 lecture, not in published work.

The hotel became widely known after Gamow's 1947 description.

The paper corrects previous assumptions about Gamow's role in originating the paradox.

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.