A case of mathematical eponymy: the Vandermonde determinant

TL;DR

This paper explores the historical development and adoption of the name "Vandermonde determinant" in mathematical literature, highlighting its origins, spread, and ongoing growth in usage.

Contribution

It provides a detailed historical analysis of how the term "Vandermonde determinant" became standard in mathematics, tracing its evolution from Vandermonde's writings to modern usage.

Findings

The term originated in France during the late 19th century.

Its adoption was influenced by citations of Cauchy and Jacobi.

The usage of the term has grown rapidly since the 1960s.

Abstract

We study the historical process that led to the worldwide adoption, throughout mathematical research papers and textbooks, of the denomination "Vandermonde determinant". The mathematical object can be related to two passages in Vandermonde's writings, of which one inspired Cauchy's definition of determinants. Influential citations of Cauchy and Jacobi may have initiated the naming process. It started during the second half of the 19\textsuperscript{th} century as a pedagogical practice in France. The spread in textbooks and research journals began during the first half of 20\textsuperscript{th} century, and only reached full acceptance after the 1960's. The naming process is still ongoing, in the sense that the volume of publications using the denomination grows significantly faster than the overall volume of the field.