Born: Paris, April 1, 1776
Died: Paris, June 26, 1831
Revolutionary Mathematician
By all accounts, Sophie Germain was a somewhat withdrawn child. She was the second of three daughters of a Parisian silk merchant, Ambroise-François Germain. One sister married a government official and the other a physician. Sophie never married, lived at home all her life, and pursued her mathematical studies with what her recent biographers term "limitless passion and devotion."*
Her first biographer, an Italian mathematician named Libri, is the source of two stories told about Germain that seem to frame her personality. As a 13-year-old, while talk of the Revolution swirled in her household, she withdrew to her father's library. There she read about Archimedes, so engrossed in his mathematical musings that he ignored a Roman invader of Syracuse, who thereupon killed him. She may have seen in Archimedes' mathematics "an environment where she too could live untouched by the confusion of social reality."** She studied mathematics on her own, and Libri relates that her parents were so opposed to her behavior that she took to studying at night. They responded by leaving her fire unlit and taking her candles. Sophie studied anyway, swaddled in blankets, by the light of smuggled candles.
On the establishment in 1795 of the Ecole Polytechnique, which women could not attend, Germain befriended students and obtained their lecture notes. She submitted a memoir to the mathematician J. L. Lagrange under a male student's name. Lagrange saw talent in the work, sought out the author, and was bowled over to discover it had been written by a woman. She continued to study, corresponding with leading mathematicians of the day.
Her mathematical work shifted from number theory to more applied mathematics. The occasion was the demonstration by a visitor to Paris, one E. F. F. Chladni, of curious patterns produced on small glass plates covered with sand and played, as though the plates were violins, by using a bow. The sand moved about until it reached the nodes, and the array of patterns resulting from the "playing" of different notes caused great excitement among the Parisian polymaths. It was the first "scientific visualization" of two-dimensional harmonic motion. Napoleon authorized an extraordinary prize for the best mathematical explanation of the phenomenon, and a contest announcement was issued.
Sophie Germain's entry was the only one. While it contained mathematical flaws and was rejected, her approach was correct. All the other possible entrants in the contest were prisoners of the ruling paradigm, consideration of the underlying molecular structure theorized for materials. The mathematical methodologies appropriate to the molecular view could not cope with the problem. But Germain was not so encumbered.
Various mathematicians helped her to pursue a new application, and she won the prize on her third attempt, in 1816. The very public prizewinning gained her some attention. But her gender kept her "always on the outside, like a foreigner, at a distance from the professional scientific culture."‡
Perhaps only a lone genius like Germain was constituted to thrive in such isolation, leaving her work of pure intellection like a beacon to later generations of women who dared to do mathematics for the joy of it.
* Louis L. Bucciarelli and Nancy Dworsky, 1980: Sophie Germain: An Essay in the History of the Theory of Elasticity (Dordrecht: D. Reidel), p. 10.
** Ibid. (But in fact she [or the history book] drew the wrong conclusion. Archimedes did not die for his absent-mindedness but was a target of the Roman soldiers precisely because he had been the "brains" behind the Syracusan defenses, directing the building of catapults and even developing a mirror system to focus light on the Roman ships and set their sails afire.)