On the Past of Mathematical ObjectsToeplitz Colloquium
Endenicher Allee 60/1-016 - Lipschitzsaal
Mathezentrum
Abstract
The question of understanding the past of a mathematical object is among the most common for those interested in the history of mathematics. However, it is often delicate to answer: even after reasonably identifying a date when the chosen object was first defined, one must trace back through time to locate earlier versions of this object and then understand the historical continuities that link these versions together. My presentation aims to illustrate these questions through the example of the genus of algebraic curves, a first definition of which can be attributed to the German mathematician Alfred Clebsch (1833–1872). I will particularly describe two distinct genealogical paths that led to this definition: one connected to the theory of abelian functions, through the work of Abel, Jacobi, Riemann, and others; the other related to the classification of algebraic curves, as explored by Descartes, Newton, Euler, and Cramer.