On the origin of Hilbert Geometry

TL;DR

This paper discusses the historical origins of Hilbert geometry, focusing on a specific letter from David Hilbert to Felix Klein that reveals the discovery process of this geometric framework.

Contribution

It provides a detailed historical account of the discovery of Hilbert geometry through primary source analysis, enriching the understanding of its development.

Findings

Reveals the context of Hilbert's discovery of Hilbert geometry

Highlights the significance of Hilbert's correspondence with Klein

Provides historical insights into the development of geometric theories

Abstract

In this brief essay we succinctly comment on the historical origin of Hilbert geometry. In particular, we give a summary of the letter in which David Hilbert informs his friend and colleague Felix Klein about his discovery of this geometry. The present paper is to appear in the Handbook of Hilbert geometry, (ed. A. Papadopoulos and M. Troyanov), European Mathematical Society, Z\"urich, 2014.