Long-term history and ephemeral configurations

TL;DR

This paper explores the contrast between long-term historical perspectives and recent focus on short-term, ephemeral mathematical configurations, emphasizing societal influences and historiographical shifts.

Contribution

It analyzes the reasons behind the shift towards studying ephemeral mathematical phenomena and advocates for a renewed interest in long-term mathematical history.

Findings

Long-term history reveals deeper connections in mathematics.

Recent historiography emphasizes societal and ephemeral aspects.

Open questions on integrating long-term and short-term historical views.

Abstract

Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral configurations of mathematicians, theorems or practices. The first part of the paper explains why this change has taken place: a renewed interest in the connections between mathematics and society, an increased attention to the variety of components and aspects of mathematical work, and a critical outlook on historiography itself. The problems of a long-term history are illustrated and tested using a number of episodes in the nineteenth-century history of Hermitian forms, and finally, some open questions are proposed.