In Pensées diverses, Sophie Germain returns several times to the theme of space or time (or even to both simultaneously), which she treats at first sight in a geometrical or even physical way, but one can also detect in it her moral conception of the passing of time, of our duration on earth and of the place that man occupies in universal creation. The most significant note concerning Germain’s understanding of space and time is the fourth one:
“Space and time are what man proposes to measure; the one circumscribes his momentary existence; the other accompanies his successive existence. These two expanses are linked by a necessary relation which is motion. As soon as it is constant and uniform, space is known by time, time is measured by space. As we have said, man does not have constancy and uniformity in him: differently modified at each moment, he is changeable, uneven, and too little durable to be the measure of duration”.
In this note, Germain offers three main ideas concerning space and time: 1) space and time are measurable, 2) they are linked by motion, and 3) man has no constancy nor uniformity. This recalls Germain’s main idea concerning intellectual judgments, i.e., the criteria of unity, order, and proportion.
An interesting article on Sophie Germain mathematical practices was written by Jenny Boucard: “Arithmetic and Memorial Practices by and Around Sophie Germain in the 19th Century”, in Against All Odds, Women’s Ways to Mathematical Research Since 1800, ed. Eva Kaufholz-Soldat and Nicola M. R. Oswald, Springer Cham, 2020, 185-230.
Reference: Germain S. (1879) Œuvres philosophiques de Sophie Germain suivies de Pensées et de lettres inédites, Librairie-Éditeur, Paul Ritti, reprinted by Elibron Classics series, 2006, Paris. (translation by Jil Muller)