She first attracted the attention of savants by her mathematical theory of Chladni's figures. By the order of Napoleon, the Academy of Science had offered a prize for the one who would "Give the mathematical theory of the vibration of elastic surfaces and compare it with the results of experiment." Lagrange declared the problem insoluble without a new system of analysis, which was yet to be invented. The consequence was that no one attempted its solution except one who, until then, was almost unknown in the mathematical world; and this one was Sophie Germain.
Great was the surprise of the savants of Europe when they learned that the winner of the grand prix of the Academy was a woman. She became at once the recipient of congratulations from the most noted mathematicians of the world. This eventually brought her into scientific relations with such eminent men as Delambre, Fourier, Cauchy, Ampère, Navier, Gauss[124] and others already mentioned.
It was in 1816, after eight years of work on the problem, that her last memoir on vibrating surfaces was crowned in a public séance of the Institut de France. After this event Mlle. Germain was treated as an equal by the great mathematicians of France. She shared their labors and was invited to attend the sessions of the Institut, which was the highest honor that this famous body had ever conferred on a woman.
The noted mathematician, M. Navier, was so impressed with the extraordinary powers of analysis evinced by one of Mlle. Germain's memoirs on vibrating surfaces that he did not hesitate to declare that "it is a work which few men are able to read and which only one woman was able to write."
Biot, in the Journal de Savants, March, 1817, writes that Mlle. Germain is probably the one of her sex who has most deeply penetrated the science of mathematics, not excepting Mme. du Châtelet, for here there was no Clairaut.[125]
Like Maria Gaetana Agnesi, Mlle. Germain was endowed with a profoundly philosophical mind as well as with a remarkable talent for mathematics. This is attested by her interesting work entitled Considérations Générales sur l'État des Sciences et des Lettres aux Différentes Époques de Leur Culture. All things considered, she was probably the most profoundly intellectual woman that France has yet produced. And yet, strange as it may seem, when the state official came to make out the death certificate of this eminent associate and co-worker of the most illustrious members of the French Academy of Sciences he designated her as a rentière—annuitant—not as a mathématicienne. Nor is this all. When the Eiffel tower was erected, in which the engineers were obliged to give special attention to the elasticity of the materials used, there were inscribed on this lofty structure the names of seventy-two savants. But one will not find in this list the name of that daughter of genius, whose researches contributed so much toward establishing the theory of the elasticity of metals,—Sophie Germain. Was she excluded from this list for the same reason that Agnesi was ineligible to membership in the French Academy—because she was a woman? It would seem so. If such, indeed, was the case, more is the shame for those who were responsible for such ingratitude toward one who had deserved so well of science, and who by her achievements had won an enviable place in the hall of fame.[126]
Four years after the birth of Sophie Germain was born in Jedburgh, Scotland, one whom an English writer has declared was "the most remarkable scientific woman our country has produced." She was the daughter of a naval officer, Sir William Fairfax; but is best known as Mary Somerville. Her life has been well described as an "unobtrusive record of what can be done by the steady culture of good natural powers and the pursuit of a high standard of excellence in order to win for a woman a distinguished place in the sphere naturally reserved for men, without parting with any of those characteristics of mind, or character, or demeanor which have ever been taken to form the grace and the glory of womanhood."[127]
The surroundings of her youth were not conducive to scientific pursuits. On the contrary, they were entirely unfavorable to her manifest inclinations in that direction. Having scarcely any of the advantages of a school education, she was obliged to depend almost entirely on her own unaided efforts for the knowledge she actually acquired. She, like Sophie Germain, was essentially a self-made woman; and her success was achieved only after long labor and suffering and in spite of the persistent opposition of family and friends.
When she was about fifteen years old, the future Mrs. Somerville received her first introduction to mathematics; and then, strange to say, it was through a fashion magazine. At the end of a page of this magazine, "I read," writes Mrs. Somerville, "what appeared to me to be simply an arithmetical question; but in turning the page I was surprised to see strange-looking lines mixed with letters, chiefly X's and Y's, and asked 'What is that?'" She was told it was a kind of arithmetic, called algebra.