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It is the autumn of 1804. Sophie Germain is twenty-eight, a woman ready to assert her worth as a serious scholar. By her own account, she had been studying the theory of numbers and had built the necessary skills to understand the theorems in Legendre’s Essai sur la théorie des nombres. Now Germain began courting the affirmation of her mathematical efforts from the pre-eminent authority in the purest of mathematical science: Gauss. Three years earlier, Gauss had captivated Germain with a new approach to study “higher arithmetic” or arithmeticae sublimiori, as Gauss called it. This is the branch of mathematics dedicated to the general study of the proper, particular properties of the integers, which now we call number theory.
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Germain-Gauss Correspondence, Appendix in this book. Letter 1.
Euclid’s key result is that if a prime divides a product, then it divides one of the factors; from this the uniqueness theorem is deduced. See: Pengelley and Richman (2006).
We know very little about Diophantus, aside from the fact that he resided in Alexandria. The only hint of his personal life comes from a riddle, which he composed in the terminology of his own algebraic problems. Diophantus was a contemporary of Julian the Apostate who reigned from 361 to 363 AD.
Ibid. On pages ix–x, Legendre wrote: «… je le donne non comme un traité complet, mais simplement comme un essai qui fera connoître à- peu- près l’état actuel de la science …».
Institut de France. Procès-verbaux. Tome II, p. 457.
Institut de France. Procès-verbaux. Tome III, p. 59.
In the nineteenth century, a mathematician was called géomètre (geometer). See Lagrange’s letter at https://gauss.adw-goe.de/handle/gauss/3552.
Germain-Gauss Correspondence, Letter 1.
Translated as Recherches arithmétiques par A.-C.-M. Poullet-Delisle. Paris: Courcier, 1807.
The Institute was reorganized and its members were assigned to four classes. Institut de France. Procès-verbaux. Tome II, pp. 621–624.
The Germain family lived on rue Sainte-Croix-de-la-Bretonnerie, no. 23.
Germain-Gauss Correspondence, Letter 2.
Ibid. Gauss wrote: “ Surtout votre nouvelle démonstration pour les nombres premiers, dont 2 est résidu ou non résidu, m’à extrémement plu.”
Letter dated 3 September 1805. See copy (in German) at https://gauss.adw-goe.de/handle/gauss/731.
Capture of Breslau in November and December 1806 during the Fourth Coalition wars. The French troops arrived on December 1806 in front of the city of Breslau, and began the siege of the city on December 9. The city surrendered on 29 December 1806.
Stupuy (1896), p. 267. Letter A in Germain-Gauss Correspondence, Appendix in this book.
Letter from General Pernety to Sophie Germain. Letter B in Germain-Gauss Correspondence, Appendix in this book.
Germain-Gauss Correspondence, Appendix in this book. Letter 6 dated 20 February 1807.
Ibid. Letter 7 dated 30 April 1807.
Les démonstrations de ces théorèmes et de ceux qui sont plus généraux sont intimement liées à des recherches délicates.
Germain-Gauss Correspondence, Letter 7 (dated 30 April 1807).
Germain-Gauss Correspondence. Letter 8.
Copy of the Germain’s letter preserved at the Niedersächsische Staats- und Universitätsbibliothek in Göttingen, Germany.
Germain-Gauss Correspondence. Letter 9 (dated 19 January 1808).
Germain-Gauss Correspondence. Letter 10, dated 19 March 1808.
Germain-Gauss Correspondence. Letter 11, dated 22 May 1809.
von Zach, Franz X. (1807). Monatliche correspondenz zur beförderung der erd- und himmels-kunde. 15. p. 507. Vesta was discovered on 29 March 1807.
A complete historical account of the discovery of the asteroids, Gauss’s work to develop his theory of planetary motion, including his communications with astronomers, is given by C.J. Cunningham, “Investigating the Origin of the Asteroids and Early Findings on Vesta.” Springer (2017).
Institut de France. Procès-verbaux. Tome III, p. 188. On 11 March 1805, Legendre presented his memoir Nouvelles méthodes pour la détermination des orbites des comètes, Paris, 1805, (XIII) in-4.
Plackett (1972), pp. 242–243.
Ibid. p. 241. Gauss letter to Olbers is dated on 30 July 1806.
Germain-Gauss Correspondence. See letter 3 dated 21 July 1805.
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