Paul Ehrenfest and the development of Kaluza-Klein theory.

In his position at Leiden, Paul Ehrenfest promoted inquiry-based dialogue among the visitors to the university, addressing a wide range of fundamental questions about physics. One such visitor, in summer 1916, was Finnish physicist Gunnar Nordstr\"{o}m, who had recently published a five-dimensional unification scheme. After discussions with Nordstr\"{o}m, Ehrenfest became interested in the question of dimensionality himself, and published a remarkable paper, ``In what way does it become manifest in the fundamental laws of~physics that space has three dimensions?'' We'll show in this talk the connections between Ehrenfest's work and the subsequent development of Kaluza-Klein theory: extending general relativity to embrace an extra dimension for the purpose of accommodating electromagnetic interactions.