Quotations in Context: Germain

“Algebra is but written geometry and geometry is but figured algebra.”

The 19th-century French author Hippolyte Stupuy wrote a wide variety of works in the arts and philosophy over his career. In 1879 he published Oeuvres Philosophiques de Sophie Germain, which included Stupuy’s new biography of Sophie Germain and a selection of Germain’s correspondence, including letters to and from Cauchy, Fourier, Gauss, Legendre, and Poisson.

The volume also included two other works by Germain. The first, Considérations générales sur l’état des sciences et des lettres, was initially published in 1833, a few years after her death. The work presented a comparison of the arts and humanities with the sciences and mathematics, arguing that the subjects had more in common than might be thought. 

Left: Engraving of Germain based on a sculpture by artist Zacharie Astruc. Public domain, gallica.bnf.fr/BnF.
Right: Photograph of Stupuy by Marius. Public domain, Paris Libraries Digital Collections.

The final work included in the volume was a previously-unpublished manuscript, Pensées diverses. As the name suggests, this manuscript contained a wide variety of thoughts on many different topics, including history, philosophy, science, and mathematics. Germain talked about some broad subjects in very abstract terms, but she also offered specific comments on individuals such as Tycho Brahe, Euler, Galileo, Kepler, Newton, Lagrange, and Laplace. Germain appears to have held an idealized view of some of these individuals; for example, she described Isaac Newton as “modest,” a characterization very different from some modern depictions of Newton: 

En parlant de Newton qui fut solitaire et modeste, qui ne chercha point à paraître, qui fit de grandes choses avec simplicité, il faut être simple comme lui, comme la nature qu’il a suivie. Cette simplicité qui le caractérise est la grandeur que son écrivain doit emprunter de lui [Germain 1879, p. 258]. 

While some of the topics are discussed in lengthy paragraphs over several pages, others are presented merely as a single short sentence. The topic quotation of this column is one of the latter, an isolated observation that appeared in the middle of a page: 

L’algébre n’est qu’une géométrie écrite, la géométrie n’est qu’une algèbre figure [Germain 1879, p. 264]. 

Reference

Germain, Sophie, and Hippolyte Stupuy. 1879. Oeuvres Philosophiques de Sophie Germain. Paris: Paul Ritti. 

“Quotations in Context” is a regular column written by Michael Molinsky that has appeared in the CSHPM/SCHPM Bulletin of the Canadian Society for History and Philosophy of Mathematics since 2006 (this installment was first published in November 2019). In the modern world, quotations by mathematicians or about mathematics frequently appear in works written for a general audience, but often these quotations are provided without listing a primary source or providing any information about the surrounding context in which the quotation appeared. These columns provide interesting information on selected statements related to mathematics, but more importantly, the columns highlight the fact that students today can do the same legwork, using online databases of original sources to track down and examine quotations in their original context.