The projective geometry of Mario Pieri: A legacy of Georg Karl Christian von Staudt

Abstract

The research of Mario Pieri (1860-1913) can be classified into three main areas: metric differential and algebraic geometry and vector analysis; foundations of geometry and arithmetic; logic and the philosophy of science. In writing this article, I intend to reveal some important aspects of his contributions to the foundations of projective geometry, notably those that emanated from his intensive study of the works of Georg Karl Christian von Staudt (1798-1867). Pieri was the first geometer to successfully establish projective geometry as an independent subject (rigorous mathematical theory), freed from all ties to Euclidean geometry. The path to this achievement began with Staudt, and involved the reformulation of the classical ideas of cross ratio and projectivity in terms of harmonic sets, as well as a critical analysis of the proof of a fundamental theorem that connects these ideas. Included is a brief overview of Pieri's life and work. © 2006 Elsevier Inc. All rights reserved.