Fragments of a History of the Concept of Ideal. Poncelet's and Chasles's Reflections on Generality in Geometry and Their Impact on Kummer's Work with Ideal Divisors

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Chemla, Karine
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212354
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Fragments of a History of the Concept of Ideal. Poncelet's and Chasles's Reflections on Generality in Geometry and Their Impact on Kummer's Work with Ideal Divisors. Karine Chemla. SIGMA 20 (2024), 066, 37 pages

In this essay, I argue for the following theses. First, Kummer's concept of ''ideal prime factors of a complex number'' was inspired by Poncelet's introduction of ideal elements in geometry as well as by the reconceptualization that Michel Chasles put forward for them i...